TACTILE SPATIAL ACUITY FROM CHILDHOOD INTO ADULTHOOD

Transcription

1 TACTILE SPATIAL ACUITY FROM CHILDHOOD INTO ADULTHOOD

2 TACTILE SPATIAL ACUITY FROM CHILDHOOD INTO ADULTHOOD: AN EXPERIMENTAL, COMPUTATIONAL & THEORETICAL EXPLORATION. By RYAN MICHAEL PETERS Hon. B.A. A Thesis Submitted to the School of Graduate Studies in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy McMaster University Copyright by Ryan M. Peters July 2013 i

3 McMaster University DOCTOR OF PHILOSOPHY (2013) Hamilton, Ontario (Psychology) TITLE: Tactile spatial acuity from childhood into adulthood. AUTHOR: Ryan M. Peters, Hon. B.A. (McMaster University) SUPERVISOR: Dr. Daniel Goldreich NUMBER OF PAGES: xii, 129 ii

4 Abstract Measurement of human tactile spatial acuity the ability to perceive the fine spatial structure of surfaces contacting our fingertips provides a valuable tool for probing both the peripheral and central nervous system. However, measures of tactile spatial acuity have long been plagued by a prodigious amount of variability present between individuals in their sense of touch. Previously proposed sources of variability include sex, and age; here we propose a novel source of variability fingertip size. Building upon anatomical research, we hypothesize that mechanoreceptors are more sparsely distributed in larger fingers. In this thesis, I provide empirical and theoretical support for the hypothesis that fingertip growth from childhood into adulthood sets up an apparent sex difference in human tactile spatial acuity during young adulthood (Chapter 2), and also predicts changes in acuity more strongly than does age over development (Chapter 3). To further understand how fingertip size could limit an individual's tactile spatial acuity, we develop an ideal observer model using neurophysiological data collected by other labs (Chapter 4). In summary, this research provides support for a novel source of variability in the sense of touch: one that parsimoniously explains an apparent sex difference, and helps clarify the source of changes in tactile spatial acuity occurring with age during childhood. iii

5 Preface This thesis is composed of five chapters. Chapter 1 introduces the reader to relevant background information, and places the empirical and theoretical work discussed later in the thesis within the context of the tactile research field. Chapters 2 and 3 are empirical studies; one is published in the Journal of Neuroscience ¹ (Chapter 2), and the other is a recently submitted manuscript (Chapter 3). Chapter 2 is included in this thesis with permission from the Journal of Neuroscience. Chapter 4 presents computational modelling of the empirical results described in Chapters 2 and 3. Lastly, Chapter 5 reviews our findings and discusses the implications of this research. This research was supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant awarded to Dr. Daniel Goldreich. This research was also supported through a graduate stipend (years 1 to 4) from the Department of Psychology, Neuroscience & Behaviour, and Ontario Graduate Scholarships (years 3 & 4). ¹ Peters, R.M., Hackeman, E., & Goldreich, D. (2009). Diminutive Digits Discern Delicate Details: Fingertip size and the Sex Difference in Tactile Spatial Acuity. The Journal of Neuroscience. 29(50): iv

6 Declaration of Academic Achievement Chapter 2. My graduate advisor, Dr. Daniel Goldreich, and an undergraduate thesis student, Erik Hackeman, designed the experiment and collected the initial portion of the data. Upon joining the laboratory, I helped design the fingertip measurement protocols, collected the remainder of the data, and was involved in all aspects of preparing the manuscript (e.g., statistical analyses and writing). Chapter 3. I was involved in all aspects of the research: experimental design, programming, data collection, statistical analyses, and writing. Dr. Daniel Goldreich also contributed to the experimental design, programming, statistical analysis, and writing. I conducted all sensory testing, and collected a large portion of the fingertip measurements. Several undergraduate students in the lab, namely, Onkar Marway, Steven Botts, Danielle Allen, James Hu, Philip Staibano, Ashley Beaulieu, and Sophia Piro assisted with collection of the remaining fingertip measurements. Chapter 4. I was involved in all aspects of the modelling presented within this chapter: programming, numerical simulations, figures, statistical analysis, and writing. Dr. Daniel Goldreich contributed to the programming and helped edit the manuscript. v

7 Acknowledgements Above all, I would like to express the utmost gratitude towards my graduate supervisor, mentor, and friend, Dr. Daniel Goldreich. His guidance and wisdom has left an enduring impact on me as a person, and also on the way I communicate, conduct, and critically think about science. Dr. Goldreich saw my potential 6 years ago when he took me on as an undergraduate thesis student, and he continues to help me launch a successful career in science today. I would also like to sincerely thank the other two members of my supervisory committee, Dr. Deda Gillespie, and Dr. Paul Faure, whose thoughtful feedback and support has been instrumental to my professional development. I would also like to thank my lab-mates in the Tactile Research Lab, Dr. Michael Wong, Andy Bhattacharjee, Luxi Li, and particularly Jonathan Tong, for their friendship and guidance during my time as a graduate student. Over the years, our office has hosted many of the most fascinating, hilarious, and meaningful discussions I have ever had. I wish you all the greatest success in your future endeavours, whichever paths you go down! Finally, I would like to thank my parents Scott and Michelle, brother Josh, and sister Sarah, as well as other close family and friends for their continued love and support. This work is lovingly dedicated to my wife Stacey, whose encouragement and devotion has sustained me through the years. vi

8 Table of Contents CHAPTER 1 1 GENERAL INTRODUCTION 1.1 Human tactile spatial acuity: a historical perspective The two point limen Ernst H. Weber Non-human primate neurophysiology Vernon B. Mountcastle Human microneuography Åke B. Vallbo & Rolland S. Johansson The grating orientation task: replacement for the flawed two-point task Kenneth O. Johnson, Robert W. VanBoven & John R. Phillips Previously reported sources of variability between individuals Fingertip size as a proxy for receptor density Overview of studies References 14 CHAPTER Preface Abstract Introduction Methods Results 23 vii

9 2.6 Discussion References 26 CHAPTER Preface Abstract Introduction Methods Results Discussion References Table and Figure Legends Table and Figures 59 CHAPTER Preface Abstract Introduction Methods Results Discussion References 95 viii

10 4.8 Figure Legends Figures 105 CHAPTER GENERAL DISCUSSION 5.1 Summary of studies The neural basis of human tactile spatial acuity Peripheral factors limiting acuity Central factors limiting acuity Implications & Future Directions Conclusion References 120 ix

11 List of Figures and Tables CHAPTER 1 Figure 1. The grating orientation task 7 CHAPTER 2 Figure 1. Perceptual data and finger size 23 Figure 2. Multivariate Bayesian analysis 24 Figure 3. Finger surface microstructure 25 Figure 4. Proposed receptor anatomy and effect of finger size 25 CHAPTER 3 Table 1. Participants who qualified for the study (n = 100), by age and sex 59 Table 2. GBF criterion value sensitivity analysis for multiple regressions between different fingertip metrics together with age (independent variables) and log tactile thresholds (dependent variable) 59 Figure 1. Bayesian adaptive procedure for threshold groove width estimation 60 Figure 2. GBF disqualification analysis and comparison between psychophysical testing protocols 61 Figure 3. Fingertip growth from childhood into adulthood 62 Figure 4. Tactile spatial acuity as a function of the six fingertip metrics 62 Figure 5. Tactile spatial acuity from childhood into adulthood 63 x

12 CHAPTER 4 Figure 1. Stimulus encoding models 105 Figure 2. The effect of fingertip size on tactile spatial acuity, from childhood into young adulthood 106 Figure 3. Decoder One Peripheral afferent responses 106 Figure 4. Decoder Two Peripheral afferent responses 107 Figure 5. Decoder Three Peripheral afferent responses 107 Figure 6. Decoder One S1 responses 108 xi

13 List of all Abbreviations and Symbols ABBREVIATIONS TAPS 2-IFC CNS GOT SA RA S1 S2 V1 RF MI GW PDF GBF Tactile Automated Passive-Finger Stimulator Two-Interval (Two-Alternative) Forced-Choice Central Nervous System Grating Orientation Task Slowly-Adapting Rapidly-Adapting Primary Somatosensory Cortex Secondary Somatosensory Cortex Primary Visual Cortex Receptive Field Modulation Index Groove Width Probability Distribution Function Guessing Bayes Factor SYMBOLS Ψ Psychometric Function a X-position of the Psychometric Function b Slope of the Psychometric Function δ Participant Lapse Rate ρ Density (# of neurons/mm 2 ) ε Strain Component (Continuum Mechanics Model) λ Wavelength of Sinusoidal Factor (Gabor Filter) θ Orientation (Gabor Filter) φ Phase Offset (Gabor Filter and Grating Stimulus) σ Standard Deviation of the Gaussian Envelope (Gabor Filter) γ Spatial Aspect Ratio (Gabor Filter) xii

14 Chapter 1 General introduction 1.1 Human tactile spatial acuity: a historical perspective Dexterous manipulation of tools is at the heart of human civilization the stone mason's trowel, the surgeon's blade, the violinist's bow. Our ability to resolve the spatial structure of objects we touch our so-called tactile spatial acuity is intimately linked with manual dexterity. This has been demonstrated physiologically by anaesthetizing mechanoreceptive afferents in the skin (Westling & Johannson, 1984), and psychophysically by the close correlation between tactile spatial acuity and manual dexterity within the same individuals (Tremblay et al., 2003; Bleyenheuft et al., 2010) 1. Because superior tactile acuity appears to bestow superior dexterity, it is vital that we understand the source(s) of variability in the sense of touch across the lifespan. In what follows, I provide the reader with some historical perspective on the measurement of tactile spatial acuity, and introduce them to the key concepts necessary for understanding the research presented later in this thesis. To help guide the reader, I begin this introduction by chronologically reviewing the work of some of the foremost researchers in the tactile field. 1 Note that, although Bleyenheuft et al., (2010) reported there was no relationship between tactile spatial acuity and manual dexterity, we suggest that they did not use the most-appropriate statistical analysis. Upon re-analyzing their dataset (extracted using GraphClick v3.0) with a partial correlation between tactile thresholds and dexterity scores, controlling for age, we found that their data in fact show a strong relationship between tactile spatial acuity and manual dexterity (rho = ; p < 10-7); thus, children with lower tactile thresholds also had higher manual dexterity scores. 1

15 1.2 The two point limen Ernst H. Weber The measurement of human tactile spatial acuity has benefited from nearly two centuries of experimental and clinical research. The earliest experimental work came from German physiologist Ernst Weber ( ). In his book, De Tactu (1834; translated by Ross, 1978), Weber describes experiments where he measured the separation between two points of contact where they began feeling like just a single point (the two point limen), as well as the ability to perceive the orientation of two points with respect to the tested body part. Weber (1834) made several important observations about how tactile experiments should be conducted. He recommended that measurements be repeated and collected from many participants. He also cautioned experimenters to use care when applying tactile stimuli, ensuring that the two points are identical in material, shape, and temperature, and that the two points are applied to the skin simultaneously, with identical application force. While Weber's early guidelines for measuring tactile spatial acuity are still generally followed today, refinements have been made to the way tactile spatial acuity is measured. 1.3 Non-human primate neurophysiology Vernon B. Mountcastle Methodological improvements were brought about by advancement in our understanding of the neural basis of tactile spatial acuity, owing primarily to combined psychophysical and neurophysiological research conducted around the mid 20th century. Much of our understanding derives from the work of American neurophysiologist Vernon Mountcastle and colleagues working with non-human 2

16 primates. The innovative approach they took towards understanding the neural basis of tactile perception was to combine peripheral and cortical single-unit recordings in non-human primates, with perceptual performance measures from humans and awake-behaving non-human primates. Mountcastle and colleagues provided comprehensive evidence for distinct afferent sub-modalities, each maximally sensitive to a particular frequency bandwidth and other properties of tactile stimulation (Talbot et al., 1968; Mountcastle et al., 1972; LaMotte & Mountcastle, 1975). They also characterized the response of neurons in primary somatosensory cortex to Hz vibrotactile stimulation (Mountcastle et al., 1969), as well as the reliance of vibrotactile perception on different cortical areas (LaMotte & Mountcastle, 1979). Mountcastle is further credited with the discovery of the columnar organization of the neocortex, a breakthrough he made while recording extracellularly from the somatosensory cortices of cats (Mountcastle, 1957; Mountcastle et al., 1957; Mountcastle, 1997). David Hubel and Torsten Wiesel later elaborated upon Mountcastle's work in their Nobel prize winning description of ocular dominance, and the functional organization of cat primary visual cortex (Hubel & Wiesel 1959, Hubel & Wiesel, 1962). Hubel originally sought a postdoctoral fellowship with Vernon Mountcastle, but the timing was awkward due to the remodelling of Mountcastle's lab; somewhat fortuitously, Hubel then joined Wiesel in Steven Kuffler's lab and began investigating cat visual cortex (Hubel, 1981). 3

17 1.4 Human microneurography Åke B. Vallbo & Rolland S. Johansson Around the same time as Mountcastle's early work, Swedish neurophysiologists Karl-Erik Hagbarth and Åke Vallbo developed a method for recording from human peripheral afferents: a technique called human microneurography (Hagbarth & Vallbo, 1967). In a series of pioneering experiments (Vallbo & Hagbarth, 1968; Knibestöl & Vallbo, 1970; Vallbo & Johansson, 1978; Johansson, 1978; Johansson & Vallbo, 1980; Johansson et al., 1980; Johansson & Vallbo, 1983; Vallbo & Johansson 1984), Vallbo and his student, Roland Johansson, recorded percutaneously (in awake humans) from the four different classes of afferents innervating the human hand, and provided the first, and still only empirically based estimates of their innervation densities (Johansson & Vallbo, 1979) values to which I will return in Chapter 4. In a fascinating experiment, Vallbo et al., (1984) even performed micro-stimulation of peripheral afferents, which caused the illusory perception of a tactile stimulus delivered to the skin. With this technique, Vallbo et al., (1984) demonstrated that afferent receptive fields mapped by mechanical stimulation of the skin corresponded well to the perceived region of illusory tactile stimulation during micro-stimulation (the projected field ), suggesting that human perception might have access to the information of individual afferents. Given the emerging neurophysiological data, researchers knew which afferents were primarily involved in spatially discriminating statically indented points used in the classic two-point task, they knew that differences in application 4

18 force between the points would affect afferent response magnitudes, and they knew the approximate spacing of tactile afferents innervating the human hand. With these newfound insights into the neural basis of tactile perception, it became apparent that the traditional method of measuring tactile spatial acuity was flawed. 1.5 The grating orientation task: replacement for the flawed two-point task Kenneth O. Johnson, Robert W. VanBoven & John R. Phillips Though several variants of the task exist, many clinical and some experimental researchers measure tactile spatial acuity using the classic two-point task, where the participant discriminates whether the skin was contacted by one point, or two points of variable separation. Using the classic two-point task, researchers often find thresholds far below that which the underlying afferent spacing should allow; in fact, on the fingertip, two points can often be distinguished from one point, even when the two points have zero separation. Additionally, classic two-point threshold estimates from the same individual are highly variable across repeated testing blocks (Van Boven & Johnson 1994b; Craig & Johnson, 2000), impeding the assessment of an individual's true tactile spatial acuity. A substantial improvement to the way tactile spatial acuity is measured was the introduction of a novel sensory task (Figure 1). The neural representation of square-wave gratings indented into the skin was thoroughly investigated in a series of papers in the early-80s (Johnson & Phillips, 1981; Phillips & Johnson 1981a; 1981b), and in the mid-90s, Van Boven and Johnson (1994a; 1994b), 5

19 provided empirical support for a new test of tactile spatial acuity: the grating orientation task. This task requires participants to discriminate the orientation of square-wave gratings indented into the skin; the spatial period of the gratings is decreased to increase task difficulty. The gratings are presented with their grooves aligned either parallel or perpendicular to the long axis of the tested body part (e.g., fingertip or lip), and the participant reports the perceived orientation. Johnson, Van Boven, and Phillips developers and namesakes of the commercially available J.V.P. Domes (Stoelting Co.) commonly used to administer the task today showed that, not only did the grating orientation task correlate more closely than the classic two-point task with the re-innervation of skin following peripheral nerve injury (Van Boven & Johnson, 1994a), it also provided a less-variable estimate of tactile spatial acuity; threshold estimates using the grating orientation task were more consistent across testing blocks, and better-correlated with the underlying receptor density of the tested body part (Van Boven & Johnson, 1994b). Both of these studies, along with more recent research (Craig & Johnson, 2000; Tong et al., Submitted), suggest that the grating orientation task provides a more rigorous measure of tactile spatial acuity than the classic two-point task. 6

20 Figure 1. The grating orientation task. A. 3D schematic of a grating used in TAPS (Goldreich et al., 2009). B. Two-Interval Forced Choice (2-IFC) version, where participants indicate which interval contained the horizontal (or vertical) grating. C. Yes-No version, where participants indicate the grating orientation (single interval). The grating orientation task also gets around another criticism of the classic two-point task: the magnitude cue (Vega-Bermudez & Johnson, 1999; Craig & Johnson, 2000; Tong et al., Submitted). The classic two-point task suffers from the existence of a non-spatial cue, resulting from the fact that two points directly apposed to one another feel qualitatively different than one point; in fact, due to skin mechanics, indenting two closely spaced points evokes fewer spikes in the peripheral afferent population than does indenting a single point at equal indentation (Vega-Bermudez & Johnson, 1999). Thus, rather than being forced to attend to the spatial conformation of the stimulus, participants can base their judgments on a difference in the magnitude of the evoked response (i.e., they can 7

21 perform the task just based on the total number of evoked spikes, rather than the spatial structure of the point stimuli). The grating orientation task avoids the magnitude cue by always having the participant discriminate gratings with equal groove width (and therefore, equal groove number), but orthogonal orientation; the participant is forced to attend to the spatial configuration of the gratings. In this thesis, we use the gold-standard grating orientation task to investigate potential sources of variability in the human sense of touch. We took Weber's (1834) advice, both in conducting psychophysical testing on large sample sizes, and in using fully-automated testing equipment (Goldreich et al., 2009) to ensure that the stimuli were applied with precise control over stimulus velocity, duration, stability, and application force. We show, for the first time, that a major source of variability between individuals in their tactile spatial acuity is the size of one's fingertip, linking perception with physical differences in the organ of touch. 1.6 Previously reported sources of variability between individuals Since its inception in the mid-90s, the grating orientation task has been used by a wide variety of researchers, investigating a wide variety of questions. From research into neurological disorders (Grant et al., 1999; 2005; Wingert et al., 2008), to the development of tactile spatial acuity in children, and its relation to manual dexterity (Tremblay et al., 2003; Bleyenheuft et al., 2006; 2010), to tactile perceptual learning (Sathian & Zangaladze, 1997; Wong et al., 2013), and the enhanced tactile acuity of blind individuals (Goldreich & Kanics, 2003; Wong et al., 2011) the grating orientation task has proven very useful. One finding this 8

22 entire body of research agrees upon is that tactile spatial acuity varies between individuals, for reasons that are largely unknown. One factor that has been reported to influence tactile spatial acuity is an individual's sex. Several studies report that tactile spatial acuity differs between the sexes, with women tending to outperform men on average (Van Boven et al., 2000; Goldreich & Kanics, 2003; Goldreich & Kanics, 2006). We found this difference between the sexes intriguing; although it is small, it is statistically significant, and using our automated equipment to administer the grating orientation task in two different studies, we found the sex difference to be identical in magnitude (Goldreich & Kanics, 2003; Peters et al., 2009 effect size = 0.18 mm). By far the most apparent, and commonly-reported source of variability is a decline in tactile spatial acuity during healthy aging (Van Boven et al., 2000; Goldreich & Kanics, 2003; Tremblay et al., 2003; Goldreich & Kanics, 2006), which has been attributed to the gradual loss of tactile receptors across the lifespan (Bruce, 1980). Although the effect of age is quite clear later in life, relatively few studies have investigated the effect of age in developing children, and there is a disagreement between the only two studies that have. Using the grating orientation task Bleyenheuft et al. (2006; 2010) found that there was an improvement in tactile spatial acuity, until roughly the age of 10, when performance saturated to young adult levels. With a less-commonly used test of tactile spatial acuity (the gap detection task, where the participant discriminates 9

23 between the presence or absence of a gap of variable width in an edge that is indented into the fingertip), Stevens and Choo (1996) showed evidence to the contrary: young children outperformed adults. 1.7 Fingertip size as a proxy for receptor density As mentioned above, a small but consistent sex difference in tactile spatial acuity had been reported previously (Van Boven et al., 2000; Goldreich & Kanics, 2003; Goldreich & Kanics, 2006), with females having finer resolution for spatial details pressed against their skin; this sex difference received little attention in the literature, and its cause was previously unknown. We reasoned that a sex difference in tactile spatial acuity could be of central origin, peripheral origin, or possibly a combination of both, and we set out to determine the source. We decided to explore the possibility that what appeared to be a sex difference to previous researchers, was due in fact to a simple physical difference in the touch-organs of the different sexes: their physical size. Anatomical studies suggest that receptor number is conserved across individuals, and that those with smaller fingers have denser receptor arrays at their fingertips (Bolton et al., 1966; Dillon et al., 2001; Nolano et al., 2003). We reasoned that women, who have smaller fingers on average due to human sexual dimorphism, might have greater receptor density on average, and thus, finer tactile acuity. Intuitively, a measure of spatial acuity should be limited by sensory receptor density just as greater numbers of pixels per inch provides a clearer visual display, the tactile neural image supplied to the CNS by the afferent population response should become 10

24 clearer if receptor density is higher. As alluring as sex differences are in popular psychology, in Chapter 2, we provide evidence that the sex difference in tactile spatial acuity is fully accounted for by an effect of fingertip size. Men with small fingertips have the acuity of women with large fingertips there is nothing special about people's sex per se in determining their tactile spatial acuity. With respect to the effect of age during development, neither of the previous studies investigating this question (Stevens & Choo, 1996; Bleyenheuft et al., 2006; 2010) took into account a variable that is concomitantly changing with age, namely, fingertip size, which we had shown significantly predicts tactile spatial acuity in young adults (Chapter 2). Due to the disagreement in the literature regarding the effect of age during childhood, and a relative dearth of research on the topic in general, we decided re-investigate development of tactile spatial acuity from childhood into adulthood (Chapter 3). We show that fingertip size is better than age at predicting changes in acuity over development. 1.8 Overview of studies We set out to explore a potential link between tactile spatial acuity (perception), and physical differences in the peripheral somatosensory apparatus. The research presented in this thesis provides support for fingertip size as a novel source of variation in the tactile perception of different individuals. In the first study (Chapter 2), we used the grating orientation task to test the fingertip size hypothesis in a large sample (n = 100) of undergraduate students. In addition to measuring each individual's tactile spatial acuity on the 11

25 dominant index fingertip, we also optically imaged the fingertip, and digitally measured its surface area. Our results demonstrate that fingertip surface area significantly predicts tactile spatial acuity, and when included in statistical analyses, completely and parsimoniously accounts for the sex difference that had previously been reported in the literature (Van Boven et al., 2000; Goldreich & Kanics, 2003; Goldreich & Kanics, 2006). In the second study (Chapter 3), we again used the grating orientation task; however, this time we investigated the development of tactile spatial acuity from childhood into adulthood (n = 116). Following our previous work, we coupled tactile threshold estimates with measurements of physical properties of each child's fingertip. Our results demonstrate that fingertip size predicted better than age the development of tactile spatial acuity from childhood into adulthood, a novel finding, and one that clarifies the previously debated effect of age on tactile spatial acuity in childhood. In a companion modelling project (Chapter 4), we used a Bayesian ideal observer model to investigate the effect of fingertip size on a theoretical basis. The model has two major components: a stimulus encoding component, which simulates the population response of peripheral or cortical neurons, and a stimulus decoding component, which uses probability theory to infer grating orientation from stimulus-epoch spike counts, and optimally performs the grating orientation task. Results of this modelling demonstrate that the fingertip surface area effect we observed empirically in children and young adults (Peters et al., 2009; Peters 12

26 & Goldreich, Submitted) emerges from the model only when certain sub-optimal assumptions are made by the ideal observer. We further speculate on the plausibility of such assumptions in real-world human perception. Taken together, the results of this research favour the hypothesis that fingertip size which likely reflects an individual's underlying receptor density provides a physical limit on tactile spatial acuity in humans. 13

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32 two-point limen. Tremblay F, Wong K, Sanderson R & Coté L (2003). Tactile spatial acuity in elderly persons: assessment with grating domes and relationship to manual dexterity. Somatosensory & Motor Research. 20: Vallbo ÅB & Hagbarth KE (1968). Activity from skin mechanoreceptors recorded percutaneously in awake human subjects. Experimental Neurology. 21: Vallbo ÅB & Johansson RS (1978). The tactile sensory innervation of the glabrous skin of the human hand. In: Active touch, the mechanism of recognition of objects by manipulation, edited by Gordon G, Pergamon Press Ltd. (Oxford) Vallbo ÅB & Johansson RS (1984). Properties of cutaneous mechanoreceptors in the human hand related to touch sensation. Human Neurobiology. 3: Vallbo ÅB, Olsson KÅ, Westberg KG & Clark FJ (1984). Microstimulation of single tactile afferents from the human hand: sensory attributes related to unit type and properties of receptive fields. Brain. 107: Van Boven RW, Hamilton RH, Kauffman T, Keenan JP & Pascual-Leone A (2000). Tactile spatial resolution in blind Braille readers. Neurology. 45: Van Boven RW & Johnson KO (1994a). A psychophysical study of the mechanisms of sensory recovery following nerve injury in humans. Brain. 117:

33 Van Boven RW & Johnson KO (1994b). The limit of tactile spatial resolution in humans: grating orientation discrimination at the lip, tongue, and finger. Neurology. 44: Vega-Bermudez F, Johnson KO (1999). Surround suppression in the responses of primate SA1 and RA mechanoreceptive afferents mapped with a probe array. Journal of Neurophysiology. 81: Weber, E. H. (1834). De tactu. Koehler, Leipzig. Westling G & Johansson RS (1984). Factors influencing the force control during precision grip. Experimental Brain Research. 53: Wingert JR, Burton H, Sinclair RJ, Brunstrom JE & Damiano DL (2008). Tactile sensory abilities in cerebral palsy: deficits in roughness and object discrimination. Developmental Medical Child Neurology. 50: Wong M, Gnanakumaran V & Goldreich D (2011). Tactile spatial acuity enhancement in blindness: evidence for experience-dependent mechanisms. The Journal of Neuroscience. 31: Wong M, Peters RM, Goldreich D (2013). A physical constraint on perceptual learning: Tactile spatial acuity improves with training to a limit set by finger size. The Journal of Neuroscience. 33:

34 Chapter Preface In this study, we wished to elucidate the source of a sex difference in tactile spatial acuity that we and others had found previously. Using the grating orientation task, we measured the tactile acuity of 100 undergraduate participants, and coupled this with surface area measurements of each participant's dominant index fingertip. Our results strongly favoured the hypothesis that fingertip size predicts tactile spatial acuity and fully accounts for the sex difference in tactile spatial acuity. In light of anatomical research, we suggest that fingertip size sets a person's afferent innervation density, and thus, the ability to perceive fine spatial details. This result provides a novel and parsimonious explanation for a significant proportion of variability between individuals in their sense of touch. 21

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41 Chapter Preface Having shown that fingertip surface area predicts tactile spatial acuity in young adults, we became interested in fingertip growth over development, and the question of whether or not children have finer acuity than adults. Only two previous studies had measured tactile spatial acuity in children, and they disagreed as to whether children possessed finer acuity than adults. Neither study measured fingertip growth; however, we hypothesized that, when fingertips grow, afferent innervation density decreases as mechanoreceptors embedded in the skin are stretched over an expanding surface. To test this hypothesis, we measured the tactile spatial acuity of children, and combined this with various measurements of fingertip size (surface area, volume, and sweat pore spacing), as well as skin surface temperature. Our results demonstrate, for the first time, that fingertip growth from childhood into adulthood predicts changes in tactile spatial acuity far more than does age. 28

42 3.2 Abstract Tactile acuity is known to decline with age in adults, possibly as the result of receptor loss, but less is understood about how tactile acuity changes during childhood. Previous research from our laboratory has shown that fingertip size influences tactile spatial acuity in young adults: those with larger fingers tend to have poorer acuity, possibly because mechanoreceptors are more sparsely distributed in larger fingers. We hypothesized that a similar relationship would hold among children. If so, children s tactile spatial acuity might be expected to worsen as their fingertips grow. However, concomitant CNS maturation might result in more efficient perceptual processing, counteracting the effect of fingertip growth on tactile acuity. To investigate, we conducted a cross-sectional study, testing 116 participants ranging in age from 6 to 16 years on a precisioncontrolled tactile grating orientation task. We measured each participant's grating orientation threshold on the dominant index finger, along with physical properties of the fingertip: surface area, volume, sweat-pore spacing, and temperature. We found that, as in adults, children with larger fingertips (at a given age) had significantly poorer acuity, yet paradoxically acuity did not worsen significantly with age. We propose that finger growth during development results in a gradual decline in innervation density as receptive fields reposition to cover an expanding skin surface. At the same time, central maturation presumably enhances perceptual processing. 29

43 3.3 Introduction In touch, as in other senses, an individual's perceptual acuity is not static throughout life. Among adults, many studies have shown a consistent decline with age in passive tactile spatial acuity, the ability to perceive the fine structure of a stimulus surface pressed against the stationary fingertip (Stevens & Choo, 1996; Goldreich & Kanics, 2003; 2006; Manning & Tremblay, 2006; Wong et al., 2011). This age-associated decline in tactile acuity may result from peripheral mechanoreceptor loss (Cauna, 1964; Bruce, 1980) and/or changes in central perceptual circuits. When a structured surface contacts the fingertip, it evokes a spatially modulated discharge pattern in the population of underlying mechanoreceptors, a peripheral neural image of the stimulus. This neural activity image is transmitted to the CNS, where it is sequentially processed within brainstem and thalamic nuclei, the primary somatosensory cortex, and areas beyond, ultimately resulting in a conscious percept. Clearly, accurate perception depends on both peripheral and central processes, but the fidelity of the initial neural image necessarily sets an upper limit on perceptual accuracy. Thus, the receptor density in a skin region ultimately constrains the spatial acuity achievable with that region, and any decrease in receptor density will result in a decline in acuity. The decline in tactile acuity with age has been well characterized among adults, but less is known about how tactile perception develops in childhood. Indeed, the literature is somewhat conflicting even on the basic question of 30

44 whether tactile acuity improves, declines, or remains unchanged with age early in life (Stevens & Choo, 1996; Bleyenheuft et al., 2006; Guclu & Oztek, 2007; Bleyenheuft et al., 2010). During childhood, both peripheral (body growth) and central (maturation of perceptual circuits) factors could plausibly cause agerelated tactile acuity changes. Two previous studies from our laboratory implicated finger size as a predictor of tactile spatial acuity among young adults. We found that index finger tactile spatial acuity improved progressively with diminishing fingertip surface area (Peters et al., 2009) and that fingertip surface area set a limit on the tactile spatial acuity that could be achieved through training (Wong et al., 2013). Together with histological data (Cauna, 1964; Bolton et al., 1966; Dillon et al., 2001; Nolano et al., 2003), these findings supported the hypothesis that cutaneous mechanoreceptors are more closely spaced in smaller fingers. If adults with smaller fingers have better tactile spatial acuity, would the tactile spatial acuity of children be even better than that of adults, and would tactile acuity decline with age as children's fingers grow? We hypothesized that fingertip growth during development would increase tactile receptor spacing (Cauna, 1964; Bolton et al., 1966), with consequent reduction in the fidelity of the peripheral neural image. However, whether tactile spatial acuity would decline with age was unclear, because concomitant CNS maturation might result in more efficient perceptual processing. To investigate, we assessed the tactile spatial acuity of participants aged 6-16 years, and measured each participant's dominant index fingertip surface area, volume, sweat-pore 31

45 spacing, and temperature. Sweat pore spacing was of interest because Merkel cell mechanoreceptors tend to cluster around the bases of the sweat ducts (Yamada et al., 1996; Guclu et al., 2008). Skin temperature was of interest because it is known to affect vibrotactile perception (Verrillo et al., 1998), and might plausibly vary with fingertip size. We found that children's tactile spatial acuity indeed worsened with increasing fingertip size; nevertheless, and intriguingly, tactile spatial acuity did not decline with age. These findings suggest that during childhood, tactile spatial perception is challenged by fingertip growth but simultaneously benefits from CNS maturation. 3.4 Methods All procedures were approved by the McMaster University Research Ethics Board. Because the participants in these experiments were minors, the participant s parent provided signed informed consent, and the participant provided signed assent. Participants We tested 116 children ranging from 6 to 16 years of age (57 girls, 59 boys). Participants were free of cuts, calluses or scars on their dominant index finger, as well as conditions that might affect their sense of touch, such as diabetes, cognitive impairment, dyslexia, or neurological disorders. We assessed each participant's hand dominance using a modified version of the Edinburgh Handedness Inventory (Oldfield, 1971). We eliminated the data of 14 children (7 girls and 7 boys) from analysis due to their poor concentration scores (see 32

46 Qualification criterion below). The data of another two participants (one 6-yearold boy and one 11-year-old boy) were eliminated as they withdrew from the study prior to completion of their sensory testing. Thus, the data reported here are from 100 participants, 50 boys and 50 girls (Table 1). Sensory Testing Participants' passive (finger stationary) tactile spatial acuity was estimated by means of the grating orientation task (GOT)(Johnson & Phillips, 1981;Van Boven & Johnson, 1994; Craig, 1999). The participant was seated comfortably with the distal pad of the dominant index finger resting over a tunnel in a table through which the tactile stimuli emerged from below. A fully automated tactile stimulator, described in detail in (Goldreich et al., 2009), was used to apply the stimuli and record the participant's responses. Acetyl stimulus pieces (0.5 diameter; milled in-house) with parallel grooves varying from 0.25 to 3.1 mm (in steps of 0.15 mm) were pressed gently onto the participant s dominant index fingertip (contact force 50 g; contact duration 1 s; onset velocity 4 cm/s). We defined vertical gratings as those with grooves aligned parallel to the long-axis of the finger, and horizontal gratings as those with grooves aligned perpendicular to the long axis of the finger. Small plastic barriers were affixed on either side of the participant s finger to prevent lateral scanning movement during testing blocks, and a force sensor was placed on the fingernail to monitor upward and downward finger movement. A computer-generated voice alerted the participant if any finger movement was detected, and such trials were 33

47 automatically discarded from analysis. Prior to sensory testing, the participant completed 20 practice trials with auditory feedback. The sensory test consisted of 4 blocks of 40 trials each. The computer program paused to require the participant to rest for at least 15 seconds after every 20 trials (halfway through each testing block), for at least 1 minute between blocks, and for at least 5 minutes at the halfway point of the experiment (after the second testing block). Sensory testing occurred via either a two-interval forced-choice (2-IFC) procedure (initial 55 participants tested) or a single-interval yes-no procedure (final 61 participants tested). The switch from the 2-IFC protocol to the single-interval protocol was made when it became apparent that young children were struggling to qualify (see Results), and we thought a singleinterval protocol with feedback might be simpler for children. In the 2-IFC procedure, participants discriminated the order of two successive grating stimuli of equal groove width but orthogonal orientation (1 s inter-stimulus interval; stimulus order chosen randomly). The participants indicated the perceived stimulus order (vertical grating first or second) by pressing one of two response buttons with the non-dominant hand. No auditory feedback was given during 2IFC testing. In the single-interval procedure, participants were randomly presented with either a vertical or horizontal grating, and were asked to identify its orientation with a button press using the non-dominant hand. Auditory feedback (one of two computer tones) was provided following each trial in the singleinterval procedure, to signal whether the participant had answered correctly or 34

48 incorrectly. In addition, a visual label was placed on the response button box to identify the vertical and horizontal grating response buttons; no such labels were present for participants tested with the 2-IFC procedure. For both the 2-IFC and the single-interval tasks, groove width was adaptively varied using a modified version of the Bayesian adaptive ψ-method (Kontsevich & Tyler, 1999; Goldreich et al., 2009). Briefly, we modeled the participant s discriminability, d-prime, as a power function of groove width, and the participant s sigmoidal psychometric function (proportion correct responding as a function of groove width, x), ψa,b,δ (x), as a mixture of a cumulative normal curve and a lapse rate term: d' b x d ' =( ) a 2 δ 1 y2 P correct ( x)=( )+(1 δ) exp dy 2 2 2π The psychometric function is characterized by three unknown shape parameters, which are initially specified by uniform prior probability densities: a (position), b (slope), and δ (lapse rate). The lapse-rate term accounts for the realistic possibility of occasional attention lapses, resulting in 50% correct response probability, regardless of groove width. The algorithm, which we programmed in LabVIEW for Macintosh (National Instruments) adaptively adjusted groove width from trial to trial, presenting the grating stimulus expected to yield the greatest information regarding the participant s psychometric function shape parameters (expected entropy minimization). We defined the participant s 35

49 GOT threshold as the groove width whose orientation the participant could correctly discriminate with 76% probability. This corresponds to x = a, at which d-prime equals 1 for the 2-IFC task (Gescheider, 1997), and at which d-prime equals 1.35 for the single-interval task. The algorithm returned the best-fitting psychometric function as well as a posterior probability distribution function (PDF) over the a-parameter (Figure 1). For the analysis, we combined the responses from all testing blocks on which the participant was clearly not guessing (see Qualification criterion), and from these combined responses we computed the participant s joint (a,b,δ) posterior PDF. For the 2-IFC task data, we marginalized the joint posterior PDF over the b and δ parameters to obtain the participant's a-parameter PDF; we took the mean of the a-parameter PDF as the participant s groove width threshold estimate. For the single-interval task, we equivalently derived the groove width at which d-prime = 1; this is the 69% correct threshold value for the single-interval procedure (Gescheider, 1997). To do this, we marginalized each participant's joint posterior PDF over the δ-parameter, plotted the best-fit psychometric function for each (a,b) pair, and interpolated to find the groove width corresponding to 69% correct performance. We then averaged this groove width across the (a,b) posterior PDF, and took this as the participant's threshold estimate. Qualification criterion Consistent performance on a psychophysical task demands sustained concentration. We screened participants for concentration by assessing the 36

50 probability that their performance could have resulted from guessing on each trial, relative to the probability that it could be described by a cumulative normal psychometric function. We call the ratio of these two probabilities the Guessing Bayes Factor (GBF), which we compute as: t 0.5 GBF t = P (r 1, r 2,..., rt Ψ a,b,δ ) P (Ψ a, b, δ )d a d b d δ a b δ where ri refers to the participant s response (correct or incorrect) on the i th trial, t is the total number of non-discarded trials in the testing block, and P(ψa,b,δ) is the prior probability density over the psychometric function characterized by parameters a, b, and δ. We chose a criterion value of GBF = 0.5 as the cut-off above which we considered a participant not to be concentrating during a given testing block. Thus, only if we were at least twice as confident that a participant was concentrating than randomly pressing buttons did we accept the participant's data from that testing block for further analysis. We applied this criterion on a blockby-block basis. We performed a sensitivity analysis to investigate the effect of different choices of qualification criterion on the statistical results (Table 2). Physical Skin Measurements We measured the surface area, volume, temperature, and sweat-pore spacing of the dominant index fingertip of each participant. To determine fingertip surface area, we scanned the distal portion of the 37

51 participant s dominant index finger with a flatbed scanner (Epson Perfection 1260). This scanning procedure is identical to that used by Peters et al., The participant placed their hand on a glass scanning surface in prone position, and the distal finger pad, from the tip of finger to the distal inter-phalangeal crease, was optically imaged at 400 dpi. Fingertip surface area was digitally measured from these images using ImageJ v10.2 (National Institutes of Health). Fingertip surface area was measured by two naive observer (P.S. and S.P.); we report the average of the observers' measurements. To measure index finger volume, we determined how much water the fingertip displaces when submerged up to the distal inter-phalangeal crease in a plastic 20 ml graduated cylinder. The cylinder was filled to the top with roomtemperature water; insertion of the finger caused a volume of water to spill out that was equal to the volume of the fingertip. We then used a USB microscope with a polarized 30X lens (ProScope HR; Bodelin Technologies) to image the waterline after the finger was withdrawn. These measurements were made digitally using GraphClick v3.0 to define the graduated cylinder tick marks above and below the water line and to measure the water line's linear position (at its lowest point) between the bracketing tick marks. To improve visibility of the water line in the ProScope images, red food colouring was added to the water and a blank piece of white paper was held against the side of the graduated cylinder opposite to the ProScope lens. This measurement was repeated 4 times and the resulting fingertip volume measurements were averaged together for use in the 38

52 analysis. To measure skin surface temperature, we used a thermistor (ON-408-PP, Omega Engineering, USA). These temperature-dependent resistors are designed for accurate skin surface temperature measurement within +/- 0.1 C. We made three separate temperature measurements: once before sensory testing began, once at the halfway point (after completion of testing block 2), and once upon completion of the sensory testing; these three measurements were averaged together for use in the analysis. To measure sweat-pore density, we coated participants' dominant index fingertip with water-based paint (Crayola Water Colours) and optically imaged the distal pad at 2400 dpi with a flatbed scanner (EPSON Perfection, 1260). We measured center-to-center sweat-pore spacing from these scans using ImageJ. Because we previously found that sweat-pore spacing between adjacent fingerprint ridges differed from sweat pore spacing within individual ridges (Peters et al., 2009), we estimated average between-ridge (μ b) and within-ridge (μw) sweat-pore spacing separately, from 20 measurements of each. Two observers performed these measurements, an author (RMP) and a naive observer (AB), and we averaged their measurements. We estimated sweat pore density, ρ (pores/mm 2), as: 1 ρ= μ μ b w Statistical Analyses 39

53 All statistical analyses were conducted using SPSS version 20 for Mac (IBM Corporation) with an alpha level of For ANCOVA, we used type III sum of squares. Reported p-values are two-tailed unless otherwise stated. For analyses of the effect of age on fingertip size metrics, and of fingertip size metrics on tactile threshold, we used one-tailed p-values, because we had directional alternative hypotheses. Specifically, we predicted that fingertips would grow with age, and that tactile thresholds would increase with fingertip size. For other analyses, including the effect of age on skin temperature and on tactile thresholds, we used two-tailed p-values, because we had no strong prediction regarding the direction of these effects. We log transformed participants tactile thresholds prior to analysis, because the measured thresholds, as well as the standardized residuals from linear regressions with measured threshold as the dependent variable, were nonnormally distributed as indicated by the Kolmogorov-Smirnov (KS) test [tactile thresholds (p < 0.001); residuals from linear regressions between thresholds and fingertip surface area (p < 0.001), volume (p = 0.004), temperature (p = 0.002), between-ridge sweat-pore spacing (p = 0.001), within-ridge sweat-pore spacing (p = 0.001), sweat-pore density (p < 0.001), age (p = 0.001)]. Log-transformation greatly improved normality, with KS tests revealing no significant violations of normality [log thresholds (p = 0.07); residuals from linear regressions between log thresholds and fingertip surface area (p = 0.096), volume (p = 0.2), temperature (p = 0.085), between ridge sweat-pore spacing (p = 0.2), within ridge sweat-pore 40

54 spacing (p = 0.124), sweat-pore density (p = 0.065), age (p = 0.181)]. In one analysis (see Results), we aggregated the data from the current study with those from Peters et al. (2009); for that purpose, we first log-transformed the thresholds from Peters et al. (2009), which improved the normality of the residuals for those data as well. We performed multiple linear regressions on log tactile thresholds with age and physical fingertip metrics as predictor variables. Because fingertip metrics were correlated with age (see Results), we calculated variance inflation factors (VIF) (Montgomery & Runger, 2010) to assess whether collinearity was not problematically high. All VIF were less than 2.3, indicating that the degree of collinearity among independent variables was well within acceptable limits (Montgomery & Runger, 2010). 3.5 Results Participant concentration and task difficulty We found that the youngest participants were much more likely to struggle with the sensory testing. A chi-squared test revealed that the proportion of participants eliminated due to poor concentration (see Methods) was significantly greater than zero among 6 year olds (X2 = 6.471, p = 0.011) and 7 year olds (X2 = 4.000, p = 0.046) (Figure 2A). Although we had hoped that the single-interval stimulus procedure would prove easier for the younger participants, a chi-squared test revealed that the proportion of participants who failed to qualify on the 2-IFC task did not differ significantly from the proportion who failed to qualify on the 41

55 conceptually simpler single-interval task (X2 = 0.186, p = 0.667) (Figure 2B). Furthermore, among qualifying participants, the mean tactile threshold on the 2IFC experiments (1.63 mm; SD = 0.60 mm) did not differ significantly from that on the single-interval experiments (1.45 mm, SD = 0.52 mm) (Figure 2C). An ANCOVA with testing protocol and sex as between subject factors, age as a covariate, and log threshold as the dependent variable revealed no significant effects of any factor (testing protocol, p = 0.117; age, p = 0.544; sex, p = 0.462). Therefore, for subsequent analyses we used the aggregate data from the two protocols. Fingertip growth during development To characterize the physical changes in the fingertip that occur during development, we conducted separate linear regressions between participant age and the six fingertip metrics collected in this study. These revealed significant positive relationships between participant age and fingertip surface area (r = 0.744, one-tailed p < 0.001; slope mm2/year), volume (r = 0.709, onetailed p < 0.001; slope ml/year), between-ridge sweat-pore spacing (r = 0.572, one-tailed p < 0.001; slope mm/year), and within-ridge sweat-pore spacing (r = 0.555, one-tailed p < 0.001; slope mm/year). There was a significant negative relationship between age and estimated sweat-pore density (r = , one-tailed p < 0.001; slope pores/mm2/year). Thus, fingertips enlarged and sweat pore spacing increased with age. Fingertip temperature did not correlate significantly with age (p = 0.529) or with fingertip surface area (p = 42

56 0.145), volume (p = 0.093), or surface-to-volume ratio (p = 0.158) (Figure 3). The effects of age and fingertip characteristics on tactile spatial acuity Next, we addressed the primary questions of this study: do age and/or fingertip characteristics significantly influence tactile spatial acuity among children? To investigate the effect of age, we first conducted a simple linear regression between age and log tactile threshold; this showed no significant effect of age on tactile spatial acuity among our participant sample (p = 0.403). We next conducted separate multiple linear regressions between each of the six physical fingertip metrics along with age (independent variables) and log tactile thresholds (dependent variable). These analyses revealed significant effects of fingertip surface area (r = 0.206, one-tailed p = 0.031) and volume (r = 0.230, one-tailed p = 0.016), and a marginally significant effect of between-ridge sweat-pore spacing (r = 0.182, one-tailed p = 0.055) (Figure 4). Age did not significantly predict tactile acuity in these analyses (p > 0.3 in all cases), although interestingly the beta weights for age were consistently negative, suggesting a non-significant trend for acuity to improve a function of age (see Table 2). Thus, among participants 6 to 16 years old, greater fingertip size was associated with significantly poorer tactile spatial acuity, whereas the effect of age was not significant. Aggregate analysis with the data of Peters et al. (2009). To further investigate whether tactile spatial acuity changes with age from childhood into early adulthood, we aggregated the data from the 100 qualifying children in the present study with that of 97 young adults whom we had tested in a 43

57 previous GOT study (Peters et al., 2009) (Figure 5). When considered alone, age again failed to predict tactile spatial acuity (Figure 5A). A univariate linear regression revealed no significant effect of age on log tactile thresholds in the aggregated dataset (p = 0.590). The results were distinct, however, when we considered age along with fingertip surface area (the sole fingertip size metric recorded for all participants by Peters et al. (2009)). A multiple regression on the aggregated log thresholds revealed significant effects of both age (t = , p = 0.014) and fingertip area (t = 4.042, one-tailed p < 0.001), with opposite directionality (Figure 5C, D). Tactile spatial acuity improved significantly with age (rate = log mm threshold decrease/year; β = ) and worsened significantly with increasing fingertip area (rate = log mm threshold increase/mm surface area; β = 0.397). This finding is consistent with the 2 intriguing hypothesis that two concomitant effects are at play during development: a progressive worsening of acuity as fingertips grow, and a progressive improvement in acuity as the CNS becomes more efficient at tactile processing; together, these factors tend to cancel the effect of age considered alone on tactile spatial acuity during development. 3.6 Discussion In this cross-sectional study, we found that tactile spatial acuity among children worsens with increasing fingertip size, as reported previously in young adults (Peters et al., 2009). Additionally, by combining the data from the present and a previous study, we discovered that fingertip size and age exert opposite 44

58 effects on tactile acuity when both variables are considered together. Statistically, at a given age, acuity worsens with increasing fingertip size; at a given fingertip size, acuity improves with increasing age. These findings suggest that two factors act concomitantly during development to influence tactile spatial acuity: fingertip growth results in a gradual decline in mechanoreceptor density, and CNS maturation results in more efficient sensory processing. Technical considerations in testing young children Some methodological observations from our experiences testing young children may prove useful to other researchers who are considering psychophysical studies with young participants. With the GBF, we were able to detect participants who were unable to concentrate consistently on the task. We found that only the 6 and 7 year old groups significantly exceeded criterion, suggesting that they were struggling to perform the task. Based on this observation, we recommended against testing such young children on the GOT and similarly demanding tactile tasks, unless the GBF is also measured. After testing 55 participants using a 2-IFC procedure, we modified our protocol in an effort to make the experiment as easy as possible to understand and perform. We tested another 61 participants using a single-interval stimulus procedure, providing auditory feedback on every trial, and identifying the response buttons with visual vertical and horizontal gratings. Despite these modifications, we found no significant differences in tactile acuity as measured on 45

59 the two tasks. In light of this equivalence in performance, and because the 2-IFC procedure is robust against criterion effects (Gescheider, 1997), we recommend that researchers use the 2-IFC procedure in future GOT studies with children, as with adults. Effect of fingertip size on tactile spatial acuity in childhood We found that fingertip size is a significant predictor of tactile spatial acuity in childhood, as shown previously in young adulthood (Peters et al., 2009). This result is consistent with the hypothesis that cutaneous mechanoreceptors become more widely spaced as the finger grows. This change in spacing would maintain sensory coverage throughout the surface of the fingertip. However, the consequent reduction in receptive field density and probable increase in receptive field size would cause a decline in tactile spatial acuity. In addition, it is conceivable that receptor depth increases with finger growth. Receptors deeper beneath the skin surface would experience less strain from a tactile stimulus (Phillips & Johnson, 1981; Sripati et al., 2006), with consequent reduction in the quality of the peripheral neural image leading to diminished acuity. Merkel cell mechanoreceptors convey the fine spatial information that underlies performance on passive tactile spatial tasks such as the GOT (Johnson, 2001; Maricich et al., 2009). Therefore, the most probable neural explanation for the decline in tactile acuity with increasing fingertip size is that the Merkel cells become more widely spaced as fingers grow. To our knowledge, no anatomical evidence currently exists regarding the change in density of Merkel cells in 46

60 humans with age. However, several studies have reported that the relatively easily visualizable Meissner's corpuscles, which mediate low-frequency vibration perception (Johnson, 2001), are more sparsely distributed in larger fingers (Bolton et al., 1966; Dillon et al., 2001; Nolano et al., 2003). In a cross-sectional anatomical study, Bolton et al. (1966) further showed that the density of Meissner's corpuscles, measured in the little finger, declined with age from childhood through adulthood. Bolton et al. (1966) propose that the decline in Meissner density during childhood is due to finger growth; they note that the continuing (yet slower) decline during adulthood is of unclear cause. We found that between-ridge sweat-pore spacing was a marginally significant predictor of acuity, whereas within-ridge sweat-pore spacing was not. Between ridge sweat-pore spacing may be more tightly linked to average afferent receptor spacing and receptive field size. Pare et al. (2002) showed that in the distal pads of non-human primates, about 80% of Merkel cells form clusters of μm in diameter that stud the basal layer of intermediate ridges; the remaining 20% of Merkel cells do not cluster together but rather form chain-like arrangements that are μm in length. Aβ afferents can branch to up to three adjacent intermediate ridges (Iggo & Andres, 1982), however, within each intermediate ridge, Aβ afferents can branch to a Merkel cell cluster surrounding the adjacent sweat duct or to a cluster or chain-like Merkel cell arrangement between adjacent sweat ducts (Pare et al., 2002; Guclu et al., 2008). Thus, the diversity of innervation targets within an intermediate ridge likely renders our 47

61 within-ridge sweat-pore spacing a poorer proxy than our between-ridge sweatpore spacing for receptive field spacing and size, and therefore, a poorer predictor of tactile spatial acuity. The effects we have observed of fingertip size on tactile spatial acuity, while significant, are weaker than those observed previously among young adult participants (Peters et al., 2009). Clearly, fingertip size is not the sole determinant of tactile spatial acuity; central factors must also play a role. In particular, while studies of conduction latencies suggest that somatosensory axon diameter and myelination become adult-like around the ages of 5 to 7 years (Eyre et al., 1991; Muller et al., 1994), central somatosensory processing circuits and cognitive circuits are presumably maturing throughout much of the age range that we have tested. Future research is needed to better-understand central contributions to the development of tactile spatial acuity. Effect of age on tactile spatial acuity in childhood and adulthood Age did not significantly affect tactile spatial acuity among the children tested in the present study, nor did tactile acuity correlate with age alone when the data from the present study were aggregated with those from the young adults tested in Peters et al. (2009). However, we uncovered a beneficial effect of age on tactile spatial acuity when we analyzed the aggregated data set with a multiple regression that included age along with finger size. Our findings suggest that, as fingertips grow during childhood, afferent receptor density declines, diminishing the fidelity of the peripheral neural image that is transmitted into the CNS for 48

62 perceptual processing; at the same time, however, as CNS pathways and circuits mature, central perceptual processing likely improves with age. Because of these opposing effects, the influence of age, considered alone, is weak. The beneficial effect of age on tactile spatial acuity becomes apparent once finger size is controlled. To our knowledge, only two other research groups have investigated agerelated tactile spatial acuity change in children. Using a grating orientation task, Bleyenheuft et al. (2006) reported that tactile spatial acuity improved with age, specifically 10 to 16 year old participants outperformed 6 to 9 year olds. Similarly, Bleyenheuft et al. (2010) found that acuity improved from ages 4 to 17 years. Using a gap-detection task, Stevens & Choo (1996) reported that tactile spatial acuity worsened with age, specifically 8 to 14 year old participants outperformed young adults (18 to 28 years old). Because of the different age ranges considered, these studies are not necessarily in disagreement; rather, taken together, the studies suggest a non-monotonic effect of age on tactile acuity, with acuity initially improving and then worsening with increasing age. Indeed, previous research from our laboratory and others shows that during adulthood tactile spatial acuity consistently worsens with age (Stevens & Choo, 1996; Goldreich & Kanics, 2003; 2006; Manning & Tremblay, 2006; Wong et al., 2011), perhaps because of progressive loss of mechanoreceptors (Cauna, 1964; Bruce, 1980). Conclusion 49

63 Our results support the hypothesis that two opposing influences act on tactile spatial perception during childhood: fingertip growth diminishes the fidelity of the peripheral neural image, but CNS maturation enhances perceptual processing. We note that the perceptual data show large individual variability (Figures 4 and 5), and indeed much variance remains unexplained (see R-squared values in Table 2). Future research will continue the important search for the sources of individual variability in tactile perception. Meanwhile, given the results of the present study, we recommend that not only age but also fingertip size be taken into account when tactile spatial acuity is compared across individuals. 50

64 3.7 References Bleyenheuft Y, Cols C, Arnould C & Thonnard JL (2006). Age-related changes in tactile spatial resolution from 6 to 16 years old. Somatosensory and Motor Research. 23: Bleyenheuft Y, Wilmotte P & Thonnard JL (2010). Relationship between tactile spatial resolution and digital dexterity during childhood. Somatosensory and Motor Research. 27: Bolton CF, Winkelmann RK & Dyck PJ (1966). A quantitative study of Meissner's corpuscles in man. Neurology. 16: 1-9. Bruce MF (1980). The relation of tactile thresholds to histology in the fingers of elderly people. Journal of Neurology, Neurosurgery, and Psychiatry. 43: Cauna N (1964). The effects of aging on the receptor organs of the human dermis, in Advances in Biology of Skin, ed. W. Montagna. (Elmsford, N.Y: Pergamon Press): Craig JC (1999). Grating orientation as a measure of tactile spatial acuity. Somatosensory and Motor Research. 16: Dillon YK, Haynes J & Henneberg M (2001). The relationship of the number of Meissner's corpuscles to dermatoglyphic characters and finger size. Journal of Anatomy. 199: Eyre JA, Miller S & Ramesh V (1991). Constancy of central conduction delays during development in man: investigation of motor and somatosensory 51

65 pathways. Journal of Physiology. 434: Gescheider GA (1997). Psychophysics: the fundamentals. Mahwah, N.J.; London: L. Erlbaum Associates. Goldreich D & Kanics IM (2003). Tactile acuity is enhanced in blindness. The Journal of Neuroscience. 23: Goldreich D & Kanics IM (2006). Performance of blind and sighted humans on a tactile grating detection task. Perception and Psychophysics. 68: Goldreich D, Wong M, Peters RM & Kanics IM (2009). A tactile automated passive-finger stimulator (TAPS). Journal of Visualized Experiments. 28: doi: /1374. Guclu B, Mahoney GK, Pawson LJ, Pack AK, Smith RL & Bolanowski SJ (2008). Localization of Merkel cells in the monkey skin: an anatomical model. Somatosensory and Motor Research. 25: Guclu B & Oztek C (2007). Tactile sensitivity of children: effects of frequency, masking, and the non-pacinian I psychophysical channel. Journal of Experimental Child Psychology. 98: Iggo A & Andres KH (1982). Morphology of cutaneous receptors. Annual Review of Neuroscience. 5: Johnson KO (2001). The roles and functions of cutaneous mechanoreceptors. Current Opinion in Neurobiology. 11: Johnson KO & Phillips JR (1981). Tactile spatial resolution. I. Two-point 52

66 discrimination, gap detection, grating resolution, and letter recognition. Journal of Neurophysiology. 46: Kontsevich LL & Tyler CW (1999). Bayesian adaptive estimation of psychometric slope and threshold. Vision Research. 39: Manning H & Tremblay F (2006). Age differences in tactile pattern recognition at the fingertip. Somatosensory and Motor Research. 23: Maricich SM, Wellnitz SA, Nelson AM, Lesniak DR, Gerling GJ, Lumpkin EA & Zoghbi HY (2009). Merkel cells are essential for light-touch responses. Science. 324: Montgomery DC & Runger GC (2010). Multiple linear regression, in Applied Statistics and Probability for Engineers. John Wiley & Sons: Muller K, Ebner B & Homberg V (1994). Maturation of fastest afferent and efferent central and peripheral pathways: no evidence for a constancy of central conduction delays. Neuroscience Letters. 166: Nolano M, Provitera V, Crisci C, Stancanelli A, Wendelschafer-Crabb G, Kennedy WR & Santoro L (2003). Quantification of myelinated endings and mechanoreceptors in human digital skin. Annals of Neurology. 54: Oldfield RC (1971). The assessment and analysis of handedness: the Edinburgh inventory. Neuropsychologia. 9: Pare M, Smith AM & Rice FL (2002). Distribution and terminal arborizations of cutaneous mechanoreceptors in the glabrous finger pads of the monkey. 53

67 Journal of Computational Neurology. 445: Peters RM, Hackeman E & Goldreich D (2009). Diminutive digits discern delicate details: fingertip size and the sex difference in tactile spatial acuity. The Journal of Neuroscience. 29: Phillips JR & Johnson KO (1981). Tactile spatial resolution. III. A continuum mechanics model of skin predicting mechanoreceptor responses to bars, edges, and gratings. Journal of Neurophysiology. 46: Sripati AP, Bensmaia SJ & Johnson KO (2006). A continuum mechanical model of mechanoreceptive afferent responses to indented spatial patterns. Journal of Neurophysiology. 95: Stevens JC & Choo KK (1996). Spatial acuity of the body surface over the life span. Somatosensory and Motor Research. 13: Van Boven RW & Johnson KO (1994). The limit of tactile spatial resolution in humans: grating orientation discrimination at the lip, tongue, and finger. Neurology. 44: Verrillo RT, Bolanowski SJ, Checkosky CM & Mcglone FP (1998). Effects of hydration on tactile sensation. Somatosensory and Motor Research. 15: Wong M, Gnanakumaran V & Goldreich D (2011). Tactile spatial acuity enhancement in blindness: evidence for experience-dependent mechanisms. The Journal of Neuroscience. 31: Wong M, Peters RM & Goldreich D (2013). A physical constraint on perceptual 54

68 learning: tactile spatial acuity improves with training to a limit set by finger size. The Journal of Neuroscience. 33: Yamada N, Kashima Y & Inoue T (1996). Scanning electron microscopy of the basal surface of the epidermis of human digits. Acta Anatomica (Basel). 155:

69 3.8 Table and Figure Legends Table 1. Participants who qualified for the study (n = 100), by age and sex. Table 2. GBF criterion value sensitivity analysis for multiple regressions between different fingertip metrics together with age (independent variables) and log tactile thresholds (dependent variable). P-values and beta weights (standardized regression coefficients) are reported in order 'fingertip metric, age'. R-squared values indicate the proportion of explained variance. Number participants (n) is indicated for each column. Lowest row: results on the data from the present study aggregated with those reported previously from 97 young adults (Peters et al., 2009). Figure 1. Bayesian adaptive procedure for threshold groove width estimation. Sensory data for two participants (P) are shown in columns: Left (panels A-C) = P1, female, age 15.9 years, fingertip surface area = mm 2; Right (panels DF) = P13, male, age 16.8 years, fingertip surface area = mm 2. (A, D) Each participant's performance plot (+ = correct response, x = incorrect response) on a single testing block. (B,E) Corresponding best-estimate psychometric function. (C,F) PDF over the a-parameter, the 76%-correct groove width. Note that, compared to P1, P13 has an upward-shifted performance plot, a rightward shifted psychometric function, and a rightward-shifted a-pdf, indicative of poorer performance; given the participants' similar ages, this performance difference is likely due to the large difference between the participants' fingertip sizes. Figure 2. GBF disqualification analysis and comparison between psychophysical 56

70 testing protocols. (A) Proportion of participants in each age bracket for whom all four end-of-block GBFs exceeded the criterion value of 0.5. (B) Proportion of participants disqualified using the two testing protocols. (C) Average thresholds of qualifying participants on the two testing protocols (error bars = 1 SD). Figure 3. Fingertip growth from childhood into adulthood. (A F). The six different fingertip metrics (A) surface area, (B) volume, (C) temperature, (D) between ridge sweat-pore spacing, (E) within ridge sweat-pore spacing, and (F) sweat-pore density), plotted against age. Black lines: least-squared linear fits. Figure 4. Tactile spatial acuity as a function of the six fingertip metrics (A F). Black lines: best-fit exponential curves from multiple regression together with age. Figure 5. Tactile spatial acuity from childhood into adulthood. Filled circles: current study; open circles: Peters et al., (2009). (A and B) results of simple linear regressions. (A) threshold vs. age. (B) threshold vs. fingertip surface area. In (A) and (B), for plotting purposes only, we have omitted the data point from the oldest participant, a year-old from Peters et al., (2009) (threshold 1.22 mm, area-adjusted threshold, 1.30 mm). (C and D) results of multiple regression with both age and surface area as independent variables. (C) surface area-adjusted threshold vs. age. (D) age-adjusted threshold vs. surface area. In (C) and (D), thresholds were respectively adjusted to the mean surface area and age of the aggregate participant sample. Black solid curves in all panels: least-squared 57

71 exponential fits. 58

72 3.9 Tables and Figures Table 1. Age Sex Girls Boys Table 2. GBF Criterion Current study Fingertip volume, age 1 (n=103) 0.5 (n=100) 0.1 (n=97) 0.01 (n=93) p = 0.025, p = 0.016, p = 0.033, p = 0.094, β = 0.277, β = 0.304, β = 0.263, β = 0.196, R2= R2= R2= R2= p = 0.049, p = 0.055, p = 0.110, p = 0.123, β = 0.197, β = 0.152, β = 0.146, Between-ridge pore spacing, age β = 0.200, R2= R2= R2= R2= Fingertip surface area, age Including young adults Fingertip surface area, age p = 0.059, p = 0.031, p = 0.073, p = 0.129, β = 0.236, β = 0.281, β = 0.223, β = 0.175, R2= R2= R2= R2= (n=200) 0.5 (n=197) 0.1 (n=194) 0.01 (n=190) p < 0.001, p < 0.001, p < 0.001, p < 0.001, β = 0.373, β = 0.397, β = 0.380, β = 0.364, R2= R2= R2= R2=

73 Figure 1. 60

74 Figure 2. 61

75 Figure 3. Figure 4. 62

76 Figure 5. 63

77 Chapter Preface In this chapter we explore the fingertip size effect on a theoretical and computational basis. Chapters 2 and 3 provide empirical support for the hypothesis that fingertip size significantly predicts tactile spatial acuity. Aggregating the data presented in these two chapters reveals the average fingertip surface area effect on tactile spatial acuity from childhood into young adulthood; it also provides an estimate of the best performance at each fingertip surface area which becomes interesting when comparing human and optimal performance. To explore the fingertip size effect on tactile spatial acuity, we simulate the responses of primate peripheral afferents and somatosensory cortical neurons, and use ideal observer analysis to model performance on the grating orientation task. We show that average human tactile spatial perception is sub-optimal in that it appears humans do not make use of all the sensorineural information available when making tactile spatial discriminations. We further speculate on biologically plausible sources for this sub-optimality. 64

78 4.2 Abstract We take for granted our ability to perceive the external world, but how does the brain accomplish this remarkable feat? Much is understood about the neural response to physical stimuli, but little about perception (how the brain interprets sensorineural activity to infer the state of the external world). Does human perception make optimal use of the available sensorineural information to form a percept? Here we describe a Bayesian ideal observer model that characterizes the theoretical upper limit of somatosensory perception. Based on the response properties of primate peripheral afferents and somatosensory cortical neurons, described by other laboratories, we simulate neuronal responses to square-wave gratings statically indented into the skin. Our model optimally infers, from this sensorineural activity, the orientation of the grating stimulus, allowing comparison to human performance on the grating orientation task. The Bayesian ideal observer when provided access to SA1 firing rates greatly outperforms average human observers on the grating orientation task. We explore the question of why, specifically, human perception is suboptimal in this sense. We show that the performance of the Bayesian observer worsens as neural firing rates grow noisier, the number of independent neurons is reduced, and stimulus integration time is shortened. We also show that the fingertip size effect emerges only when the ideal observer makes particular sub-optimal assumptions about the afferent responses. Whether and to what degree these limitations characterize human sensory processing remains to be determined. 65

79 4.3 Introduction We sought to synthesize previously collected neurophysiological and anatomical data into a unified (Bayesian) framework, focussing on the processing of cutaneous input originating from the fingertips. With this model, we attempt to better-understand our ability to perceive the orientation of edges indented into the skin, and specifically, to develop a theoretical understanding of the empirically observed effect of fingertip surface area on human tactile spatial acuity (Peters et al., 2009; Wong et al., 2013; Peters & Goldreich, Submitted). Ideal observers are theoretical devices that enable us to quantify the amount of information available on a given task. They also provide us with a benchmark against which we can compare human performance. The standard of optimality is useful when trying to interpret human perceptual abilities, particularly when constraints imposed on the quality of the information provided to the ideal observer have an anatomical and physiological basis. If human perception is sub-optimal, it becomes interesting to consider the possible source(s) of this sub-optimality; we pursue this idea throughout this chapter. These models have two major components: an encoding model (also referred to in the literature as a generative or forward model), which simulates the sensorineural response to a given stimulus, and a decoding model, which utilizes probability theory to infer the most probable stimulus given the evoked sensorineural response. The use of ideal observer analysis has a rich history in the study of human visual and auditory perception, dating back to the 1950 s. For instance, Wilson 66

80 Geisler and colleagues have elegantly applied ideal observer analysis to study a number of visual phenomena including photon detection and the discrimination of stimuli ranging from dot patterns to complex objects and natural scenes (e.g. Geisler, 1984; Geisler & Davilla, 1985; Geisler, 1989; Geisler & Albrecht, 1997; Geisler et al., 2001). One interesting application which is the approach we take here is sequential ideal observer analysis (Geisler, 1989), with the goal being to characterize the transformation of the information content at sequential levels of a given sensory system. Here we wish to extend these ideas to the study of human tactile spatial perception by examining two different levels of the somatosensory system: the SA1 afferent population, and area 3b neurons in the primary somatosensory cortex (S1). It is generally accepted that the slowly-adapting type 1 (SA1) primary afferent population carries the highest-resolution spatial representation of edges in contact with the skin (for review see Johnson, 2001). In the early 1980 s, Phillips and Johnson (Johnson & Phillips, 1981a; Phillips & Johnson, 1981a; 1981b) demonstrated that the SA1 afferent population has greater spatial modulation in its response profile than any other receptor type when bars and gratings are indented into the distal finger pads of macaque monkeys. Furthermore, Phillips and Johnson (Johnson & Phillips, 1981a; Phillips & Johnson, 1981a; 1981b) demonstrated that only the SA1 afferents could account for human psychophysical performance. For this reason, and for simplicity, here we limit our analysis to the SA1 population response. Rapidly-adapting type 1 (RA1) primary afferents 67

81 which are the only other receptor class possessing small enough RFs and high enough innervation density to resolve details on the order of 1 mm likely contribute less information to spatial perception, and may in fact interfere with, and reduce the high-resolution spatial signal sent through the SA1 afferents (Bensmaia et al., 2006; 2008b). To simulate the primary afferent population response, we use a continuum mechanics model of the skin. We implement the model described by Sripati et al., (2006b), which generalizes the original continuum mechanics model proposed by Phillips and Johnson (1981b), allowing the stimulus to vary over two-dimensions rather than only one. This model simulates the strain profile resulting within the skin in response to indented spatial patterns (see Figure 1A). SA1 afferents are activated by strain applied to the region of their receptor end organs, Merkel cellneurite complexes. SA1 responses are well-predicted by a linear translation of the strain value sampled at the depth of the receptor end organs (Phillips & Johnson,1981b; Sripati et al., 2006). The model requires assumptions to be made about the composition of the skin (that it is a homogeneous and isotropic elastic medium, and that it is infinite in extent from the receptor s point of view); nevertheless, it accurately predicts single-unit firing rates to a wide range of tactile stimuli (mean Pearson's r = 0.87; Sripati et al., 2006b). In addition to modeling the peripheral representation of grating stimuli, we also model the responses of neurons in somatosensory cortex (area 3b). Similar to the early stages of visual processing, a sub-population of area 3b cells have RFs 68

82 consisting of an excitatory central region and one or more flanking inhibitory regions (DiCarlo et al., 1998; DiCarlo & Johnson, 2000; Sripati et al., 2006a; Bensmaia et al., 2008b). Just like V1 simple-cells, the receptive fields of orientation selective S1 neurons are well-characterized by oriented Gabor spatial filters (Bensmaia et al., 2008b). Previous ideal observer modelling based on the responses of single neurons in S1 indicates that human bar orientation perception can be accounted for by the spike counts of the most orientation selective neurons (Bensmaia et al., 2008b). Here we attempt to characterize the area 3b population response to the square-wave grating stimuli commonly used to test human tactile spatial acuity, and also extend this analysis beyond the single-cell, to a population code. To simulate the response of area 3b neurons, we use Gabor spatial filters that are fit directly to spike counts recorded from area 3b neurons in response to indented bar stimuli (courtesy of Dr. Sliman Bensmaia). 4.4 Methods 197 undergraduate participants (95 men, 102 women; age range = 6.6 to 27.9; mean age = 16.2; SD = 4.8) tested in two previous studies (Peters et al., 2009; Peters & Goldreich, 2013) were used to test the predictions of the ideal observer model. All sensory testing methods are described in detail in Chapters 2 and 3. Stimulus encoding models We aim to characterize the information content of SA1 afferent, and S1 (area 3b) sensorineural population responses. Figure 1 provides a schematic 69

83 depiction of the SA1 and S1 encoding models used in our ideal observer analysis. This section describes how we simulated stimulus-epoch spike counts based on previously reported neurophysiological data. Peripheral afferent encoding model To model the peripheral afferent population, we begin by defining a receptor grid (the black dots in Figure 1C). To do this, we draw a 10 mm by 10 mm square grid with a given receptor (node) spacing. To avoid having the receptor grid occasionally align perfectly with the grating edges, and to more realistically simulate SA1 sampling positions in the skin (e.g., see Figure 6 from Johansson & Vallbo, 1980), we added Gaussian jitter to the x and y coordinates of each node in the square grid. The SA1 receptor x-y sampling positions are also defined in terms of their depth within the simulated elastic medium (i.e. their position within the basal layer of the epidermis), z. According to the continuum mechanics model, the strain profile dampens and becomes less spatially modulated with increasing depth (because the skin acts as a low-pass mechanical filter). Following Sripati et al., (2006b), we modeled the expected firing rate of each SA1 afferent, f SA1 (S ), given the stimulus, S, as a positive-rectified linear transformation of the strain value sampled at each afferent s x-y-z position, ε xyz, + f SA1 (S )=[a (ε xyz b)]. (Equation 1) 70

84 Here the constants a and b represent the best-fit sensitivity (slope) and threshold (intercept) of the simulated SA1 afferents, respectively. To generate realistic firing rates however, we need to take into account the noise present in all neural responses. The noise inherent in SA1 firing rates is remarkably low, and will be characterized here by a Gaussian probability distribution function, P (r SA1 f SA1 (S ))= 1 σ SA1 2 π ( exp 2 r SA1 f SA1 (S ) 2 σ SA1 2 ), (Equation 2) where P (r SA1 f SA1 (S )) is the conditional probability of observing the firing rate, r SA1, given the expected firing rate, f SA1 (S ). Furthermore, the relationship between SA1 noise magnitude, σ SA1, and the expected firing rate f SA1 (S ), is well-approximated by (Vega-Bermudez & of an SA1 afferent, Johnson, 1999), 0.21 σ SA1=0.45 f SA1 ( S ). (Equation 3) This SA1 noise relationship was determined empirically by VegaBermudez & Johnson (1999) for a 200 ms stimulus duration; thus, for the simulations reported here (see Fig 2), we derived the relationship between the mean and standard deviation of SA1 afferent firing rates over a 50 ms temporal interval, given as: 0.21 σ SA1=0.3 f SA1 (S ) n (Equation 4) where n is the number of 50 ms intervals in the total stimulus duration (i.e., if the 71

85 total duration is 1000 ms, then n = 20). We chose not to show SA1 noise model curves for stimulus durations longer than 100 ms, because the model already farsurpassed human performance at this point. Therefore, to simulate the firing rate of an individual SA1, r SA1, we randomly sampled from the Gaussian density function given in Equation 2, with the standard deviation given by Equation 4. SA1 noise was added in this manner to each afferent firing rate, i r SA1 (which will here on be indexed by superscript, i). We represent the final population response with the vector, r SA1, which contains the responses of all activated SA1 afferents. Finally, we recognize that the neural representation relevant to perception is probably not the peripheral afferent population response. Neural responses in the cortex tend to have much greater variability: the variance in firing rate is nearly equal to the expected firing rate (characteristic of a Poisson process; Sripati et al., 2006a). In our analysis, we consider the possibility that cortical neurons responsible for making perceptual decisions simply have direct access to the peripheral afferent representation (i.e. implying 1:1 mapping of peripheral RFs to cortical RFs), but that the noise on their spike counts is generated by a homogeneous Poisson process, where, f SA1 ( S ) P (r SA1 f SA1 (S ))= e f r SA1 SA1 r SA1! (S). Primary somatosensory cortex encoding model 72 (Equation 5)

86 The cortical representation we consider here is that of area 3b of S1. We adopt a linear spatial filter approach for generating cortical spike counts: a commonly used method for modelling neural responses of V1 simple cells (Daugman, 1988). Here we assume that area 3b RF properties are static with respect to time, although, the time course of excitation and inhibition in these neurons is known (DiCarlo et al., 1998, DiCarlo & Johnson, 2000, Sripati et al., 2006a); how temporal dynamics in RF structure affect information content is an interesting question for future modelling efforts. We generate S1 responses by creating a 10 x 10 mm image of the grating strain profile, S, obtained from the continuum mechanics model (Sripati et al., 2006b), and model the cortical response as a positive-rectified linear transformation of the dot product between each neuron's RF and S. Therefore, the expected firing rate of neuron i is, [[ f isa1 = α e 2 2 u +γ v 2 2σ +ϕ ) ] S +β ] ( 2 π u λ + 2 cos (Equation 6) where, u=( x xc ) cos(θ)+( y y C ) sin(θ), (Equation 7) and u= ( x x c ) sin (θ)+( y y C ) cos(θ). Here, xc and (Equation 8) y c are the x and y components of the center position for each modeled neuron. The parameters of the Gabor function (in Equation 6) 73

87 are the wavelength of the sinusoidal factor, λ, the orientation of the filter, θ, the phase offset, ϕ, the standard deviation of the Gaussian envelope, the spatial aspect ratio of the Gabor, σ, and γ, which determines the ellipticity of the Gabor bands. Once again, Poisson firing rate noise was added to the expected response (i.e., f S1 (S ) ) as per Equation 4. Because it is unclear how many neurons are used by the CNS to represent a grating stimulus, the question of how sparse to make this representation becomes highly relevant. We know there are diminishing returns to the accuracy of inference as the number of neurons on which the inference is based increases. As the number of neurons in the representation increases, performance of an unbiased estimator will asymptotically approach the Cramer-Rao lower bound (Paradiso, 1988; Dayan & Abbott, 2001), the theoretical apex of performance given the constraint of tuning curve shape. However, perceptual decisions may rely on the activity of only a few highly selective neurons (Geisler, 1997; Olshausen & Field, 2004; Bensmaia et al., 2008b). To investigate this, here we parametrically vary the area 3b population size. Fitting the encoding models to neurophysiological data To fit the peripheral afferent model we created custom LabVIEW fitting programs that determined the set of parameters that provided the least-squared fit between the simulated SA1 afferent responses and the average SA1 modulation index reported over a range of grating groove widths (Phillips & Johnson, 1981a; 74

88 we fit their Figure 8 for the static phase of indentation middle panel). The spatial modulation index (MI) is a measure of how sensitive SA1 afferents are to edges, and is calculated as: ( MI = r max r min r max +r min ) (Equation 9) In this equation, r max and r min correspond to the maximum and minimum observed firing rates, respectively, for a given SA1 afferent when a square-wave grating is stepped in 0.2 mm increments across the afferent's RF, indenting the grating at each step. Due to the enhanced edge sensitivity of SA1 afferents, r max will occur when an edge is indented into the afferent's hotspot (skin site of maximum excitability), and r min will occur when a groove (i.e. no edge) overlies the afferent's hotspot. Phillips & Johnson (1981a) recorded the average SA1 modulation index for groove widths ranging from 0 (smooth) to 3 mm; however, we only fit from 0.5 to 2 mm because this provided better fits in the region that matters most (the observer's threshold is always less than 2 mm for the simulations reported here). For the peripheral afferent model, the parameters that we fit were receptor depth, sensitivity, and threshold, as well as the relative weighting of maximum compressive to maximum tensile strain. We took the weighted average between maximum compressive and maximum tensile strain as the candidate strain component that model SA1s transduced, because this provided better fits to the neurophysiology than using either strain component independently. Previously, 75

89 Phillips & Johnson (1981b) favoured maximum compressive strain, and Sripati et al., (2006b) favoured maximum tensile strain; thus, both strain components are strong candidates according to the literature. Seeing as there is no reason to think that only one of these strain components must be involved, we took the weighted average between maximum compressive and maximum tensile strain as the candidate strain component here. The best fit parameters were: indentation depth = 1200, sensitivity = 190, threshold = , max. compressive-to-max. tensile weight = With this set of parameters, the model fits the average SA1 modulation index during the static phase of indentation well (Max. rate fit: Pearson's r = 0.982; Min. rate fit: Pearson's r = 0.598; Mean Pearson's r = 0.79). It is also important to note the large error bars on the mean values shown in the original figure from Phillips & Johnson (1981a; see their Figure 8). For the cortical encoding model, we used macaque (Macaca mulatta) area 3b receptive fields provided to us by Dr. Sliman Bensmaia (University of Chicago). The responses of cortical neurons to single bars indented at various orientations and positions relative to the RF center were fit with Gabor spatial filters (Bensmaia et al., 2008b). This fitting was done with custom MATLAB programs written by Dr. Bensmaia and colleagues. Because these Gabor RFs were derived from recordings made while indenting single bars, not grating stimuli, and we wanted to generalize our model to gratings as well as other spatially-structured stimuli like points or embossed letters, we decided to use the strain profile as input to the Gabor (rather than use a binary image of the stimulus, as in Bensmaia 76

90 et al., 2008b). Our reasoning was that the strain profile might better capture nonlinear changes that occur due to skin mechanics when more than one bar is indented (i.e. a square-wave grating or the letter A). To do this, we adjusted the response of the Gabors using strain profiles of a bar as input (new method) such that it best-matched the response of the Gabors using binary images of a bar as input (original method); to accomplish this, we found the scale factor to apply to the output of the new method, that provided the least-squared fit to the output of original method. Again using custom LabVIEW fitting software, we found that a scale factor of 0.09 gave the best fit. When we apply this scale factor to the response of the Gabor using grating strain images as the input, we get stimulusepoch spike counts that agree well with empirically observed spike counts (Burton & Sinclair, 1994; Sinclair et al., 1996; Personal communications with Dr. Sliman Bensmaia). Stimulus decoding models To examine information at different levels of the somatosensory system we analyze the performance of Bayesian decoding models that are provided with either peripheral afferent or cortical responses. Optimal performance is obtained by making decisions based on evaluation of the likelihood function or competing model likelihoods, which provides an unbiased estimate of latent stimulus parameters (Green & Swets, 1966; Dayan & Abbott 2001). Here we analyze the performance of three decoding models, each differing in terms of the assumptions made about the sensorineural data. 77

91 Decoder One (Optimal) We begin with a decoder that knows everything (e.g., with the SA1 encoding model it knows the receptor x-y-z positions, thresholds and sensitivities, as well as the stimulus indentation depth, and duration). This is equivalent to stating that Decoder One knows the stimulus-response function for each of its neurons, a common assumption made in previous probabilistic population code models (e.g., Jazayeri & Movshon, 2006; Gold & Shadlen, 2007). To determine the probability of each grating orientation for each trial, we calculate the probability of observing the population response, r, given each possible grating orientation. This was calculated for the case of Gaussian noise as, P (r f i (S ))= P (ri f i (S ))= i i 1 σ SA1 2 π ( exp ri f i (S ) 2 2 σ SA1 2 ) (Equation 10) and for the case of Poisson noise as, P (r f i (S ))= P (r i f i (S ))= i where, f i(s) ri f i (S ) ri! e i (Equation 11) P (r i f i (S )) is the likelihood for the i-th neuron in the population, f i (S ) is the stimulus-response function of that particular neuron, and r i is the observed firing rate. To simulate the grating orientation task we indented a horizontal grating (of variable spatial frequency and randomized phase) 1 mm into the simulated skin, and had the ideal observer determine whether the sensorineural data (i.e., the afferent population response during the static phase of indentation, 78 r ) was

92 more probable given a horizontal or a vertical grating orientation. These two hypotheses about orientation (vertical and horizontal) are really compound statistical models, not simply hypotheses, because an optimal inference regarding grating orientation needs to incorporate sub-hypothesis for all the possible grating spatial frequencies and phases, and needs to marginalize over these so-called nuisance parameters (parameters other than grating orientation in this case). Accordingly, we computed the likelihood of the horizontal orientation model (M1) as, P (r M1)= P (r i GW, ϕ, M1) P (GW, ϕ M1) GW ϕ, (Equation 12) i and the likelihood of the vertical orientation model (M2) as, P (r M2)= P (r i GW, ϕ, M2) P (GW, ϕ M2). GW ϕ (Equation 13) i Finally, to compare models, we computed the likelihood ratio (LR) between them, LR= P (r M1). P (r M2) (Equation 14) which is equivalent to the posterior odds, given that we applied a uniform prior over the models. If this ratio is greater than 1, the observer has correctly identified the horizontal grating orientation; this same decision variable was used for all simulations. GW and ϕ correspond to all possible grating groove widths (0.5 to 2 mm, in 0.5 mm steps), and all possible grating phases (from 0 to 2xGW, in steps of 0.2 mm), respectively. Decoder Two ( Knows it is uncertain regarding receptor location) 79

93 The next decoder we simulated is uncertain about the x-y position of each of its neurons, and knows this to be the case. To deal with its uncertainly, Decoder Two marginalizes over a square grid of hypothesized positions for each receptor (with a fixed 0.1 mm node spacing), centered on each receptor's actual position. To parametrically vary the strength of Decoder Two's assumption, we varied the hypothesized ranges for possible receptor locations (the size of the square hypothesized receptor grids) from +/- 0.3 to 0.9 mm. This marginalization should recover much of the information not provided to Decoder Two (i.e., the actual receptor positions); thus, little difference should be observed between the performance of Decoders One and Two. For Decoder Two, the model likelihoods are calculated as (note the additional sum over possible receptor locations), P (r M )= P (r i xy, GW, ϕ, M ) P ( xy, GW, ϕ M ). xy GW ϕ i (Equation 15) Decoder Three (Mistaken about receptor location) The final decoder we consider is incorrect about the x-y position of each of its neurons. Sub-optimally, Decoder Three assumes fallacious receptor x-y positions drawn from 2D Gaussians, each centered on the actual receptor grid positions used to generate the population response. To parametrically vary the strength of Decoder Three's assumption in a manner similar to varying the range 80

94 of possible receptor positions for Decoder Two, we varied the SD of these 2D Gaussians from 0.3 to 0.9 mm. (in 0.2 mm steps; the various curves are depicted in Figure 4A and 4B). The likelihood computation is therefore identical to that of Decoder One; however, Decoder Three is just slightly-mistaken about the position of each neuron's RF center, and thus, slightly-mistaken about the response to expect. Decoding model assumptions We did not implement prior expectation for any particular grating orientation, groove width, or phase uniform priors were used over these stimulus parameters. All three decoders assumed that the stimulus-epoch spike counts of different neurons within the population were conditionally independent, given the stimulus. The decoders also knew the structure of the noise to be Gaussian or Poisson (i.e., Equation 2 or 5). Model simulations All simulations were carried out using LabVIEW 11 (National Instruments). To quantify each decoding model's performance, we used the method of constant stimuli and linearly interpolated the groove width resulting in 69% correct performance (where d-prime = 1 for the single interval version of the grating orientation task simulated here). The human thresholds used for comparison also correspond to performance where d-prime = 1 (Peters et al., 2009; Peters & Goldreich, Submitted). We estimated the ideal observer's proportion correct with the method of constant stimuli. For the peripheral afferent 81

95 encoding model, we simulated 1000 yes-no trials for each groove width (grating phase randomized across trials), under each parameter setting (e.g., stimulus duration). For the cortical encoding model, we attempted to more closely capture the real-world scenario where each observer deploys a particular set of cortical neurons, and bases its decisions on that particular set of neurons throughout testing. Accordingly, we reduced the number of trials to 50 per groove width and repeated the interpolation 20 times each time with a unique Gabor population; in the results, we report the mean threshold estimate across the 20 blocks, as well as +/- 1 standard error. Because human perception might integrate only a portion of the evoked sensorineural information to reach decisions (e.g., 100 ms worth of spiking activity, even though 1000 ms worth was available), we varied the duration of the stimulus integration window from 50 to 1000 ms. 4.5 Results First, we investigate performance of the three decoding models using the peripheral afferent encoding model, and attempt to capture the previously reported effect of fingertip size (Peters et al., 2009; Peters & Goldreich, Submitted). Then we examine Decoder One's (optimal) performance when basing its decisions on cortical (area 3b) responses, rather than peripheral afferent responses. The effect of fingertip size on human tactile spatial acuity By aggregating the data from two previous studies involving a total of 197 participants (Peters et al., 2009; Peters & Goldreich, Submitted; Figure 2A), and calculating the average groove width threshold in 50 mm 2-wide fingertip surface 82

96 area bins, we obtain an estimate of the average effect of fingertip size on human tactile spatial acuity (Figure 2A blue curve), as well as an estimate of the best possible performance in each fingertip size bin (Figure 2B diamonds). A linear regression on the fingertip size bin averages revealed a significant effect of fingertip surface area (r = 0.88, one-tailed p = 0.004; slope = 0.15 mm/cm 2; 95% CI = 0.06 mm/cm2 to 0.24 mm/cm2); an additional linear regression on the best thresholds in each fingertip size bin also revealed a significant effect of fingertip surface area (r = 0.91, one-tailed p = 0.002; 0.16 mm/cm2; 95% CI = 0.08 mm/cm2 to 0.25 mm/cm2). Thus, it is quite clear that a relationship exists between fingertip surface area and tactile spatial acuity, but under what circumstances would an ideal-observer predict this? From the aggregate data (Peters et al., 2009; Peters & Goldreich, Submitted; Figure 3A), we derived a theoretical relationship between human fingertip surface area and average SA1 afferent spacing. Given that we know the average index fingertip surface area was mm 2, and that an estimate of mean SA1 receptor spacing at the fingertip is 1.2 mm (Johansson & Vallbo, 1979), and if we assume that SA1 receptor number is actually fixed between individuals (an extreme statement of the fingertip size hypothesis), then the average SA1 density at the fingertip is, 1 2 =0.694 SA1s /mm 2 (1.2 mm/ SA1) (Equation 16) and thus, the estimated total number of SA1 afferents in the average fingertip is, 83

97 mm SA1s /mm 241 SA1s. (Equation 17) If we assume that the number of SA1 afferents is conserved between individuals, then we can estimate an individual's SA1 density at the fingertip as, Estimated SA1 Density= 241 Fingertip Surface Area (Equation 18) and estimate their SA1 spacing at the fingertip as, Estimated SA1 Spacing= 1 SA1 Density (Equation 19) Using the above equations, we took the entire range of aggregated fingertip surface areas ( to mm2), and converted that to a range of corresponding estimated SA1 spacings at the fingertip (0.89 to 1.46 mm). We then plugged this range (0.9 to 1.5 mm in 0.3 mm steps) of estimated fingertip SA1 spacings into the model to see if it would evoke the fingertip size effect reported previously (0.15 mm/cm2 Peters et al., 2009; Peters & Goldreich, Submitted). Decoder One Peripheral Afferent Responses It is clear that the optimal decoder regardless of using peripheral (Gaussian) or cortical (Poisson) noise, and regardless of reductions in the window of sensorineural integration (i.e., the stimulus duration) appears to be affected very little by changes in fingertip size. For all the curves depicted in Figure 3, the average slope of the linear regression line was just a 0.02 mm threshold increase / cm2 surface area, a much shallower slope than the effect of fingertip size on human tactile spatial acuity reported previously (Peters et al., 2009; Peters & 84

98 Goldreich, Submitted). For the various Poisson noise model curves (Figure 3, grey scale lines), reducing the stimulus integration window caused a gradual upward curve shift; however, the slope remained essentially flat (mean slope = 0.02 mm/cm2). The closest-to-human regression slope was obtained with Poisson noise and an integration window of 50 ms (0.04 mm/cm 2); however, this slope still falls below the 95% confidence interval for the human regression slope (0.06 to 0.24 mm/cm2). Results of the Poisson noise model do suggest the tantalizing possibility that the very best human performance might in fact be optimal (as seen by the close correspondence between Decoder One's curves and the best performance in each fingertip size bin in Figure 3). Decoder Two Peripheral Afferent Responses Next we wanted to simulate a decoder that can optimally deal with uncertainty in receptor location, and recover performance levels similar to that of the optimal Decoder One. We did this by having Decoder Two make hypotheses about each afferent's x-y position; for each afferent, Decoder Two set up a square grid of hypothesized locations, which was always centered on the true afferent location, but ranged in size +/- 0.3 mm to +/- 0.9 mm (with a constant 0.1 mm grid step size). Decoder Two then marginalized over all possible afferent locations (as well as grating phases and groove widths), to find the probability of each grating orientation (see Methods). Figure 5 shows 100 ms stimulus duration model curves when the size of the square grids of hypothesized receptor locations was increased from +/- 0.3 mm to +/- 0.9 mm (grey scale curves). It is clear that 85

99 Decoder Two attains the performance level of Decoder One, and there is very little effect of changing the range of hypothesized locations. The average slope for the curves shown in Figure 4 was 0.04 mm/cm2. As we expanded the range of the possible receptor positions to +/- 0.9 mm, the slope of the regression line approached the human regression slope (0.11 mm/cm 2); the average regression slope for the remaining three curves shown in Figure 4 was 0.02 mm/cm 2. Decoder Three Peripheral Afferent Responses Having shown that Decoder Two was able to recover much of information it was not provided (i.e., the actual receptor positions) by marginalizing over a grid of possible receptor positions, we wanted to simulate one final decoder that was simply mistaken about the x-y positions of its neurons. Due to this, Decoder Three was also mistaken about the stimulus-epoch spike count to expect from each neuron, given the tactile stimulus distorting its ability to decode the peripheral afferent response. To vary the amount by which Decoder Three was mistaken, we varied the SD of the 2D Gaussians, centered on the actual receptor x-y positions, from which the fallacious x-y positions were drawn (see Figure 5A and 5B; curves generated using SDs of 0.3 mm to 0.9 mm, in 0.2 mm steps). The different panels of Figure 5 were generated using 1000 ms (Figure 5A) and 100 ms (Figure 5B), respectively. Increasing the SD had a pronounced effect on the model's threshold, elevating the curves into the range of average human performance on the grating orientation task. The average slope for the 1000 ms model curves (Figure 5A) was 0.03 mm/cm2, which was shallower than the 86

100 average effect of finger size; thus, when Decoder Three integrated spikes over a 1000 ms window, the effect of increasing error in receptor position elevated the model thresholds, but failed to replicate the fingertip size effect. For the 100 ms model curves (Figure 5B), the average slope was 0.13 mm/cm 2, and ranged from 0.05 mm/cm2 with an SD of 0.3 mm, up to 0.26 mm/cm2 with an SD of 0.9 mm; thus, when Decoder Three integrates spikes over a 100 ms window, the effect of increasing error in receptor position reproduced the average fingertip size effect, and even approximately replicated the 95% confidence interval for the human regression slope value when the SD is varied from 0.3 to 0.9 mm (the various curves in Figure 4B). Based on this analysis, it appears that the effect of fingertip size on tactile spatial acuity might be the by-product of two sources of suboptimality on behalf of human observers: 1) a limited (e.g., 100 ms) temporal stimulus integration window, and 2) slight error in the CNS's ability to know the exact skin region covered by each of its afferent RFs (i.e., receptor position). Decoder One Cortical Neuron Responses Lastly, we examined performance of the optimal decoder when it based its decisions on the responses of area 3b cortical neurons, rather than SA1 afferents. When modelling the cortical responses, the question quickly becomes: on how many cortical neurons does the CNS base its decisions? As the number of neurons in the representation increases, performance of an unbiased estimator asymptotically approaches the Cramer-Rao lower bound (Paradiso, 1988; Dayan & Abbott, 2001); to show this, we considered a range of neuronal population sizes 87

101 (see Figure 6), increasing the population size until performance saturated at what is likely the Cramer-Rao lower bound for the area 3b cortical model described here (Figure 6B). Due to the inhomogeneity of tuning curves used in our model (because we used actual area 3b RFs, not idealized Gaussian envelopes), we could not readily derive the Cramer-Rao lower bound analytically, and increasing the population size much beyond 1225 neurons led to memory allocation issues; however, performance appears to converge around 0.6 mm. We note that Paradiso (1988) simulated up to 10,000 neurons in a cortical hyper-column model for visual orientation discrimination, and performance still did not asymptote entirely. Just how many neurons are required to form a perception remains a mystery, but by determining the population size that results in average human performance given the 100 ms stimulus-epoch spike counts simulated here (Figure 6A), we estimate the number to be around 200 independent neurons. The exact number of neurons will depend on the stimulus integration window used by the observer, as well as the degree of correlated firing between neurons within the population. 4.6 Discussion Throughout evolution, nervous systems have devised myriad ways of converting energy impinging on the body into neural activity. A major challenge the nervous system faces is decoding this neural activity to reconstruct the external world (perception). An increasingly popular viewpoint of the way nervous systems solve this problem often called the inverse problem lies within the framework of probability theory. Population responses may represent 88

102 probability distributions over sensory variables within the CNS, and this information might be passed along to sequential processing centers in a hierarchical structure. The optimal way of manipulating probability distributions is Bayesian inference: this has led to its resurgence in modern neuroscience (Knill & Richards, 1996; Doya et al., 2008). How probabilistic computations could be implemented in biological systems remains an interesting and open question, although plausible theories do exist (e.g. Rao, 2004; Averbeck et al., 2006; Jazayeri & Movshon, 2006; Gold & Shadlen, 2007; Deneve, 2008; George & Hawkins, 2009). Sources of sub-optimality in human perception Unlike the combination of multiple sources of sensory information (e.g., visual and haptic), which humans appear to do optimally (Ernst & Banks, 2002; Ernst & Bülthoff, 2004), the utilization of sensorineural information within each given sensory modality does not appear to be entirely optimal. An interesting question arises at this point: what is the source(s) of this sub-optimality? Here we show that performance of the model worsens as neural noise is increased (e.g., Gaussian vs. Poisson noise), as the number of independent neurons is decreased, and as the temporal window of sensorineural integration is reduced. How well do these factors characterize human perception? An increase in noise certainly occurs in the somatosensory system, from the periphery (where noise is well-approximated by a narrow Gaussian distribution: Vega-Bermudez & Johnson, 1999) to area 3b (where noise becomes Poisson, or Poisson-like: Sripati 89

103 et al., 2006a). In terms of neuronal population size, whether one considers afferent receptor density or the number of neurons used for neural decoding in the CNS, reducing the size of the population conveying information about the stimulus results in degraded performance. Finally, the temporal window of integration is another factor that could limit human perception; although we indented grating stimuli for 1000 ms, it is likely that the central neural decoder only based its decisions off a fraction of the total sensorineural data. There is converging evidence in vision as well as olfaction that the window of temporal integration might be around 200 to 300 ms (for review, see Uchida et al., 2006). Limited research has attempted to determine the temporal window of integration for the sense of touch, and never before has this been investigated for human grating orientation task performance. Interestingly, 200 to 300 ms is in close agreement with the findings of Bensmaia et al., (2008a), who showed a slight decrement in performance on a tactile bar orientation discrimination task when the stimulus duration was reduced from 400 ms to 100 ms. Contrary to this 200 to 300 ms window, Craig (1980) has shown that performance on a tactile pattern recognition task only begins to worsen at stimulus duration below about 50 ms, suggesting the 50 ms is the temporal integration window. Ultimately, the temporal window of stimulus integration might be tightly linked to natural exploration strategies (e.g., saccade duration for vision or possibly contact time during haptic exploration for touch), and could depend on various factors including task difficulty or a cognitive emphasis on performance speed or accuracy, as well as biological 90

104 constraints such as adaptation, leaky integration of sensory information, and correlated neural activity (see Uchida et al., 2006). To determine the temporal window for the grating orientation task, future researchers should use progressively shorter stimulus durations in experiments with human participants until performance worsens significantly, indicating that the true temporal window of stimulus integration is being impinged upon. Emergence of the fingertip size effect on human tactile spatial acuity The modelling results presented here suggest that the previously observed effect of fingertip size on human tactile spatial acuity (Peters et al., 2009; Peters & Goldreich, 2013) is the byproduct of sub-optimal decoding on behalf of the CNS. Only when we introduced error into the expected response of the modelled neurons did the ideal observers' performance approach that of average human observers. Furthermore, only when we reduced the stimulus duration from 1000 ms to 100 ms did a positive slope occur for the model curves which approximates the previously reported relationship between fingertip size and tactile spatial acuity (Peters et al., 2009; Peters & Goldreich, Submitted). Recently, suboptimality in human perception has been linked to the inability of the neural decoder to precisely read out probabilities from its likelihood function (Putzeys et al., 2012). Here our decoders optimally read out from their likelihood functions; however, whether the fingertip size effect would appear when a sub-optimal likelihood read-out function is used (Putzeys et al., 2012), should be investigated in future modelling efforts. 91

105 We note that, although we introduced error in the expected response by making the decoder slightly mistaken about the location of its RFs, this could have been done in other ways. For instance, the decoder could equivalently be mistaken about the anatomical depths, sensitivities and/or mechanical thresholds of its afferents. Exactly what information the neural decoder has, or could possibly have access to is a crucial question for future researchers to consider. Though it is often assumed that the neural decoder has access to the tuning functions of every neuron (e.g., Jazayeri & Movshon, 2006; Gold & Shadlen, 2007), exactly how this is possible is unclear. Does the timing of individual spikes matter? We limit our analysis exclusively to a stimulus-epoch spike count code, even though additional information is presumably available if the ideal observer takes spike timing into account (Rieke et al., 1999). There is evidence that perception of vibrotactile amplitude relies on a firing rate code in primary somatosensory cortex (Harvey et al., 2013), and here we show that a firing rate code sufficiently accounts for human discriminability on the grating orientation task. Some researchers have proposed that the perception of vibrotactile frequency also relies on a firing rate code (Luna et al., 2005); however, there is emerging evidence that the frequency of vibrotactile stimulation is coded in a spike timing reliant manner, and that the neural code used in somatosensory cortex is multiplexed, with vibration amplitude coded by firing rate at long time scales, and vibration frequency coded by spike timing at short time scales (Mackevicius et al., 92

106 2012; Harvey et al., 2013). Interestingly, first spike latency alone has been shown to accurately encode the direction of forces applied to the skin (Johansson & Birznieks, 2004), though the extent to which first spike latency could accurately encode spatial structure (e.g., grating orientation) is not known. We do not rule out the relevance of spike timing in decisions based on surface microgeometry (e.g., discriminating between fabrics), which is a spatial property that cannot be resolved with an SA1 spatial code; this can be illustrated quite clearly by our inability to discriminate between fabrics when they are statically pressed against the skin only when we scan our fingertips over fabrics are they discriminable. Scanning of fabrics elicits a unique spectral signature of vibration across the the skin surface (Bensmaia & Hollins, 2005; Manfredi et al., 2012), which is likely captured primarily by RA2 (a.k.a. Pacinian channel, PC) afferents in the precise timing of action potentials (Mackevicius et al., 2012). However, for the static grating task modelled here, a spatially modulated spike count code seems appropriate. Indeed, spike count decoders become spike timing decoders as the temporal resolution of the decoder is increased sufficiently, allowing only a single spike to occur in each time step (e.g. see Rieke et al., 1999); thus, our modelling framework could readily be extended to consider models of primary afferent spike timing (e.g. see Dong et al., 2013). A fundamental question in neuroscience remains for future research: what is the temporal window over which sensorineural integration occurs and is it task-dependent? Conclusions 93

107 Here we present an ideal-observer for the study of human tactile spatial acuity. Over the years, a plethora neurophysiological data has been collected detailing the neural response to tactile stimuli; with this work, we sought to synthesize this data into a unified model. Over 30 years ago, Phillips & Johnson (1981b) expressed the need for such a modelling framework (i.e., one that enables examination of the spatial neural representation of complex stimuli when receptor spacings and sensitivities are not uniform ; p. 1202). Although here we have chosen, out of simplicity, to use uniform receptor sensitivities, the model we present offers a scaffolding upon which progressively more complex, and biologically realistic models of tactile perception may be built. Our ideal-observer model suggests that human tactile spatial acuity is suboptimal in that all the sensorineural information available appears not to be utilized. Future work is needed to pin-down what information is actually used in perceptual decisions and to test predictions of this model; for example, how does human performance on the grating orientation task degrade when stimulus duration is reduced, or how does adaptation of particular human and model neurons within the population alter perception? 94

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115 4.8 Figure Legends Figure 1. Stimulus encoding models. (A) The 2D continuum mechanics model (Sripati et al., 2006b), in which the grating stimulus is defined as a series of indented point loads that together cause a spatially modulated profile of strain within a simulated elastic medium. (B) The Gabor spatial filter model for S1 responses (Bensmaia et al., 2008b). To simulate S1 responses, we took the dot product between each neuron's RF (Gabor) and the grating strain profile. (C) Neuronal sampling grids. For the 2D continuum mechanics model, strain profiles are sampled at each afferent's x-y-z position (black dots) in the fingertip. For the S1 model, we centered Gabors on each neuron's location (only two Gabors shown for illustration). (D) The response of each neuron is then linearly scaled to find the expected firing rate, and noise is added to the expected firing rate that is characteristic of either peripheral afferents (Vega-Bermudez & Johnson, 1999), or cortical neurons (Sripati et al., 2006a). Figure 2. The effect of fingertip size on tactile spatial acuity, from childhood into young adulthood. (A) Aggregated human grating orientation task performance data reported in two previous studies from our lab (Peters et al., 2009; Peters & Goldreich, Submitted). Solid line is the least-squares fitting line for the young adult dataset (Peters et al., 2009), and the dashed line is the least-squares fitting line for the child dataset (Peters & Goldreich, Submitted). (B) By discretizing fingertip surface area into 50 mm 2-wide bins, we obtained an estimate of the mean (dotted blue curve), and best (diamonds) human performance at each finger size. 102

116 The blue shaded region denotes +/- 1 SD. Figure 3. Decoder One Peripheral afferent responses. Human data from Figure 2B are overlaid on model curves for visual comparison. The two red curves depict SA1 noise simulations using 100 ms (solid), and 50 ms (dashed) stimulus durations. The grey scale curves depict Poisson noise simulations using a range of stimulus integration windows: 1000 ms (black), 500 ms, 250 ms, 100 ms, and 50 ms (lightest grey) windows shown. Figure 4. Decoder Two Peripheral afferent responses. Human data from Figure 2B are overlaid on model curves for visual comparison. Shown here are model simulations using a 100 ms stimulus integration window. The grey scale curves depict Poisson noise simulations, each generated using a different range of hypothesized receptor x-y locations centered on the actual location: +/- 0.3 mm (black), to 0.9 mm (lightest grey), in 0.2 mm steps. Figure 5. Decoder Three Peripheral afferent responses. Human data from Figure 2B are overlaid on model curves for visual comparison. Shown separately are model stimulations using two different stimulus integration windows: 1000 ms (A), and 100 ms (B). The grey scale curves depict Poisson noise simulations, each generated using a different standard deviation for the 2D Gaussian distributions from which the fallacious receptor x-y locations are drawn: 0.3 mm (black), to 0.9 mm (lightest grey), in 0.2 mm steps. Figure 6. Decoder One S1 responses. (A) Psychometric functions from model simulations using different populations sizes. Grey scale curves depict the various 103

117 population sizes used. The number of neurons used is listed above each curve. (B) Interpolated 69% correct groove width threshold as a function of the number of neurons. Note the diminishing returns on increasing population size. 104

118 4.9 Figures Figure 1 105